This motion shows up in some styles of Karate (opening movement of several Shotokan kata - Bassai Dai, Jiin, Jion, Jitte) and some Kung-Fu styles. What does it represent?
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This ritual is called Bao Quan (抱拳), literally meaning "Fist Wrapping", and is a common etiquette derived from (but not exclusive to) Chinese Martial Arts. It is not necessarily a bow, but rather a salute. Traditionally, this is practiced by:
There are two traditional explanations.
The left palm with its 4 fingers represent the 4 nurturing elements: Virtue, Wisdom, Health, and Art. These symbolize the spirit of martial arts. The left thumb is slightly bent to imply one should never be arrogant or self-centered. The right fist symbolizes rigorous practice. Since the right hand is clenched in a fist, it symbolizes attack, while the left, being virtuous and disciplined, stops the attack, symbolizing self-discipline and restraint.
The left hand symbolizes the 5 (major) lakes of China, the fist representing the 4 seas surrounding China. The two hands together show the unity of martial artists. This is exemplified in the saying 五湖四海皆兄弟 (I believe wu hu si hai joe xiongdi, but I don't know much Chinese), which means "The people of the 5 lakes and 4 seas are all brothers." This, I'm lead to understand, is commonly taught as a meaning to Bak Mei practitioners. This also has ties to the Hung Society, but this trends off-topic.
Edit: I have also heard numerous other explanations from various instructors in different styles of Kempo and Wushu, ranging from the "Right is war, left is peace" to the meeting of Taoist (right) and Buddhist (left) cultures in unity. The two I list as traditional (above) come from sources who've been very helpful in researching things in the past. These edit-included excuses tend to be perpetuated down less reputable lines.
There are many reasons for this action. It is, by the way, not the opening movement of a form, but a salute, a ritualistic motion. Here are a few reasons:
In the system that I teach in, the left hand symbolizes the mind, the right symbolizes the body. We have three bows as you progress through training:
This hand posture is also found associated with the sho chiku bai (pine, bamboo, plum) formations as seen at this link: http://www.skski.net/sho-chiku-bai-mon.html. More details about that can be found there, as well.
In Morihei Ueshiba's book on aikido talks about the sho chiku bai throughout its pages, but doesn't discuss the hand postures: http://www.amazon.com/Secret-Teachings-Aikido-Morihei-Ueshiba/dp/1568364466/
Robert Trias of Shuri-ryu karate mentions Sho Chiku Bai. He doesn't necessarily stress it, at least not within his Pinnacle of Okinawan Karate book. However, all of the Shuri-ryu katas (and perhaps others) end with each of these hand positions. The connection between them is not well explained, though (in my experience).
It seems a lot of myths are being perpetuated here. Many answers are correct - but in martial context can only apply to a greeting as might be done when entering or exiting the kwoon, or greeting Sifu.
But as to Japanese kata, the context of the question, and also Korean poomsae/hyung, the covered fist has absolutely nothing to do with greetings, war and peace, thank you, hello, good bye, subservience, gratitude, weaponless and empty hands, or any of that nonsense. It is not to say that the covered fist can't have these meanings in context other than kata. But in kata, these meanings do not apply at all.
There are several ways to debunk the concept of greetings, et al, as used in kata or poomsae, and I suspect the same is true even in Chinese taolu (kata).
What is kata?
To start, it is necessary to understand what is the purpose for kata. If it is believed anything other than self-defense, then that means going back to sensei (or sabumnim, in Korean styles), and asking for the correct answer. Some styles implement a bit of symbolism, but in classical Japanese and Okinawan kata, it is all about self-defense. For those reading this answer who are not in a classical Japanese or Korean style, perhaps your style might employ a bit of symbolism, such as in World Taekwondo (WTF), whose new set of forms are all about presentation, and not at all about self-defense.
What is covered fist salute?
Next is to understand the traditional meaning of the hand-over-fist, which is a common etiquette form in China - but not in Korea or Japan. At one time in history, maybe it was commonly practiced in the latter two cultures. But by and large, this is relegated to Chinese culture. Hence, my earlier reference to kwoon (dojo) and Sifu (sensei).
From a Japanese / Okinawan perspective, I can offer little historical analysis, as my knowledge there is limited. But I can say that greetings now - and then (when the forms were invented) - are almost always by way of a bow, not by a covered fist. The Okinawans were adamant that in their forms, there is a always practical use for everything. Neither greetings nor symbolism of the sort are practical. There are no wasted movements at all. Everything performed is related to movement to support self-defense. The form itself may take on some symbolism, but never the movements within.
As a corollary, there are two kinds of Karate: there is "do" and there is "jitsu". The "do" is the part about the way of life, and to this extent is probably where the myth of the greeting had been introduced. The "jitsu" part concerns itself with the science of fighting, and any sort of symbolism is patently dismissed. Note that the "jitsu" part came about long before the "do" part. Nevertheless, anyone practicing the "do" part of Karate can still live the life of Karate and even sit around their campfires ruminating about the symbolism of the covered fist, and still get in the practice for the actual applications they represent when they get back to the dojo.
From a Taekwondo (or any classical Korean style, like Tang Soo Do or Hwa Rang Do, etc) perspective, the same applies as it does for Japanese styles, but there is more thought about why these styles use the covered fist, and here also, the same greetings myth is spread about. Its forms go back no further than 1955, so, one might consider the mindset back in 1955 when the forms were being drawn up. (Ok, give or take a few years; it didn't happen over night). Why would the Koreans implement such a movement that is not culturally relevant, at a time when they were desperately trying to re-Koreanize their culture when they became liberated from the Japanese? Why would they adopt any cultural influence from Japanese martial arts? (Answer: because they were probably never taught properly by their Japanese instructors, most of whom did not hold many Koreans in any regard as they were seen as an imperialized culture, who themselves were never held in very high regard by the Okinawans). The Koreans simply used what they borrowed from their Japanese style influences, and if any sort of greeting or existential symbolism was adopted into the Korean forms, it was because that was all they knew. This we know from reading the Kukkiwon textbook or General Choi's encyclopedia, and there, such is not covered at all. If it was a deliberate decision to remove the practical aspects of covered fist and change the meaning to something like a greeting, then, besides copping out on technique, they will have short-changed self-defense instruction. And further, they'd have documented this in their respective tomes. As it is, such is left primarily undiscussed.
Debunking lesson #1: Culturally confused greeting
When we perform a kata, it seems well established that the student bows to the instructor, or to the judges, and then begins the kata. But why do so with another culturally-confused greeting? This makes sense to everyone? That is like greeting your boss every morning with "Good morning! Bon jour!"
Debunking lesson #2: Greeting the enemy
As to the symbolism of greeting both the instructor/judge and the enemy, I say, no one ever greets their adversary. Or thanks them. That happens in the movies, but not in real life. There are millions of fights on YouTube alone, high school fights, gang fights, riots, CCTV prison fights, street fights, sibling fights, grannies duking it out over coupons in the express lane, kids duking it out over an ice cream cone, ad nauseum. Not a single one shows either combatant showing any sort of respectful courtesy before the pugilistic activity begins. (Have I seen all said millions of videos? No. Still looking though.) Maybe my not having seen an example of two otherwise angry combatants mutually respecting one another which makes this is a myth is a logical fallacy?
Perhaps, the adversary is respected, much like we respect a venomous snake's ability to kill us. We do not greet the snake, we do not thank the snake for its... whatever it is we're supposed to be thanking it for. We do not throw up a symbol of war and peace at it. We leave the damned thing alone!
And when leaving the damned thing alone doesn't work, that is where the system of kata sort of takes over. Greetings, dialog, turning the other cheek, tact, diplomacy - all of that has failed. We now have to defend ourselves from great bodily harm. We do not bow to the enemy, nor do we issue a symbol of culturally-dependent meaning to our adversary. If so, we could justifiably replace it all with a "Yo, sup!" with a pinky and index finger pointed at the shoulder. Or maybe we cut it back a little, and use the less formal Chinese method of fist and rigid hand. It's a greeting, right? And that means, women use the right hand to cover the left fist, right? Or did they tell you about that little detail? Because that IS the greeting protocol, yes? Yep, I'm going down this road:
Debunking lesson #3: Men vs women vs friends vs enemy vs funerals
Here's the primer: Men cover their right fist with the left hand; women do the opposite and cover left with right. They do this in formal settings when things are normal.
But there's more: It's considered a sign of anger (some say akin to "flipping the bird") when a man covers left with right, and when a woman covers right with left. Unless, of course, they are all at a funeral, at which, the protocol to greet is the same as if in anger when not at a funeral (so men politely cover left with right, and women cover right with left...) Ok, Asian society has a lot of strange protocols. Question is, which one would the kata be following?
Does your sensei allow you to change hands based on whether you are a man making a polite greeting, a woman making a polite greeting, a man saying "screw you", a woman saying "screw you", or either of you exhibiting a funeral rite? (I suspect not the latter. Just going out on a limb here, but it seems reasonable to dismiss this case.)
Debunking lesson #4: Smile!
And what about the facial expression: aren't you taught never to show emotion? Why would you offer a polite greeting without smiling? Why would you give a neutral facial expression while telling someone to have sex with himself? Why would you remain silent while making a polite greeting, telling someone to kiss off, or expressing regret at the loss of their loved one?
STILL think the covered fist has anything to do with greetings in kata?
Debunking lesson #5: The numbers game
Why, then, do so few kata have this greeting? I don't know the numbers in Japanese forms, but for taekwondo (kukkiwon) there are 8 Palgwe, 8 Taeguek, and 9 yudanja forms - a total of 25 forms - same in ITF. About two use the "greeting", the numbers are not all that different in Karate styles. So now this begs the question: why are we greeting in a couple of kata, but not the others?
Debunking lesson #6: Weapons
And what of the idea that the hands represent something that is weaponless? There is a clear contradiction in your forms. How many times have you been told to perform this technique or that technique in such a way so as not to let the opponent optimally see your incoming technique or weapon? In other words, why show you are weaponless, and then split seconds later do something to hide your weapons?
Debunking lesson #7: Leo Tolstoy
And what of the idea that the covered hand represents war and peace? In our kata, our goal is to dispatch our adversary. It might be by way of a throw, or a choke, or a vital area in the throat to kill. This idea that the greeting before the form begins having to do with war and peace seems contradictory with the actions about to be performed merely seconds away from said philosophical statement of... war and peace.
Debunking lesson #8: Slavery
And what of subservience? Come on. We are not indicating subservience to our adversary. Do we really need to go there?
The answer is, the covered fist that is reminiscent of greeting, gratitude, subservience, anger, or sympathy in China is not the same thing in our forms. Such requires a complex social setting context considerations which is not applicable to self-defense. Such is an easy mistake to make: "Looks like a greeting, so, must be a greeting, so, not gonna use my brain and explore further."
So... then what is it?
Answer: it's an opening move.
The kata has to start somewhere. So we begin our bunkai by considering the posture we make when we begin the form. At that moment, we have been attacked. Our opponent is white, and we are black. White moves first, and has done so, and now it is our move.
Recall the rules of forms analysis (and if you don't remember, refer to the link, below): If you touch yourself in a form, that represents you touching your opponent. Fists are grabs (or they can be punches; but in a covered fist, I think we can all agree it's not a punch). Open hands are anything BUT a grab, but they can secure an opponent's grab so we can effect a technique like a S-lock, or something.
(And, let's get into the nitty-gritty details of the "covered fist". We have a right-handed fist, and the left hand is wrapping the fist; or the left hand is straight and rigid, as would be the two cases in a Chinese greeting. There is significant difference in bunkai; the covered fist means more tightly holding onto the opponent, whereas the straight hand could mean passive touch of the opponent. Either way, consider the differences and alternatives in your bunkai.) And is the fist such that the top of the hand can balance a tea-cup, as is sometimes called for in some schools; or is the top of the fist more diagonal and the index finger's knuckle pointing upward? Consider these alternatives in your bunkai as well.
Now we can start to imagine several PRACTICAL uses for the covered fist, and not some useless greetings or existential meanings. Without example of kata that uses covered first, it's hard to be specific about application, so, I'll generalize here. If it doesn't apply to your kata, then keep analyzing.
Application #1: Attack from behind, move to the side
Ever notice how sometimes we move left or right immediately after the covered fist "greeting"? (Ok, I'll stop calling it a greeting...) In this case, we imagine we have had one or both hands grabbed from behind. Settle low (bending knees), bend elbows; this allows us to move the grabbed hands to the front. You may concern yourself with either of the opponent's hands, it doesn't matter. But now you've got his hands in front of you (and notice, you're not reaching so far forward with the covered fist as to throw you off balance, because his arms are surely not long enough to do this!) you hold your right hand in a fist and clench it (that is a classic movement which opens the wrist ever so slightly, giving you advantage to release yourself from the grip). With your left hand (covering the fist means holding his grabbing hand onto yours: you now WANT him to keep grabbing so you can effect the next movement). You turn to the side and... well the rest depends on the next movement in the kata.
Application #2: Attack from behind, move to the front
Sometimes, we can move to the front when grabbed from behind. Consider much of the scenario from application #1; this time, though, when we bring his hands in front of us, we can step to the side with the opposite foot we brought the hand around; then we step forward with what will be the inside leg, and that hopefully off-balances him which is useful, say, for a throw.
Application #3: Attack from front, issue a wrist lock (#1)
Here we assume we're grabbed by either/both wrists. There are a couple of variations here.
With both hands lowered and unfisted, lift upwards, and catch his grab in the web of your right hand. As you lift higher, you grab his wrist, as if you take his pulse. This represents the fist in the covered fist. Now with your left hand, hold his hands there so he can't let go (you want to finish him off, yes? Violent, but effective. If we didn't hold him there, he could let go and try again.)
As you hold him there, the rest depends on the kata's movement, but one general possibility is that with his grab being covered (bound) by your left hand (remember, covered fist means left touches right, which means, we are touching opponent), you are in perfect placement for a wrist lock, like kotegaishi. You've got his wrist, so, it's one example of a kotegaishi.
Application #4: Attack from front, issue a wrist lock (#2)
Similar to application 3, this one doesn't have you catch his grab in the web of your hand. Rather, you let him grab you; raise your grabbed hand (clenched fist, to ready for atemi to the face, if opportunity provides), cover (secure) his grip with your left hand. From here, you can move circularly to the left or right, which twists the wrist into a lock (Aikido-ka will immediately recognize this as nikkyo). From here, you can easily transform into sankyo, or some other technique like a takedown, throw, lock, or pin.
Application #5: Reversal
If your sensei is worth his or her salt, you will be taught that one of the things your kata teaches is "reversals". This could be one of those techniques where you are the attacker administering a choke or a lapel grab (either could be inferred from the covered fist technique.) The covered fist here isn't itself the reversal; rather, the techniques that follow assume your adversary is reacting to your choke/grab, and, you are being reversed. So that is out of scope of the question, except to say that it is a vaild point of study (bunkai).
Application #6: Preparation for a throw
By now you should be getting the idea that Karate and Taekwondo are anything but punches and kicks. There's grappling, throws, locks, and pins. Yes, throws are a part of Karate and Taekwondo, and if you aren't learning them, then your instruction is incomplete. The covered fist in a standing position of feet together is a perfect position to get into for a shoulder throw: your fist is cross-grabbing your opponent's other shoulder, the covering hand is securing the shoulder. Of course, the covered fist in of itself isn't the throw - that would depend on the next movements in the kata. If you were to slide forward, or tenkan into a 180 degree turn, that strongly suggests a throw is intended here.
Well, there you go: 6 applications, and long commentary (sorry about that), debunking the notion that a covered fist is any kind of greeting.
I strongly recommend to read the book "The Way of Kata", by Lawrence Kane and Kris Wilder.
Also, you ought to watch and read books and videos by Iain Abernethy and John Burke. All of these authors provide logical and realistic explanations for many of the things we do in kata. It applies to Korean styles as well. If your instructor is feeding you a line about symbolism, that is a red blinking neon flag that the instructor doesn't have a clue about what the movement is, and is afraid to admit s/he doesn't know.
If you don't have access to the book at the moment, here is a link or two which espouses some of the principals in the book, which you can read immediately here. I'm in no way endorsing the sites or the dojos they represent or the instructors; I'm merely sourcing examples used in my answer:
Also, about Chinese covered fist:
Some more relevant and good reading:
The fist is symbolic of fighting or war, the open hand is covering it showing that we come in peace, but are ready for war if that is what the other person wants or brings. The open hand with the fingers straight is also similar to an extended open hand ready to be shaken. With the fingers outstretched towards the other person it's basically showing that we prefer to be at peace over war.
There are of course many other meanings attached to it as well, but that is basically what is taught in the gung-fu system that I learned.
I always get them mixed up, but I used to know a Northern Shaolin form that started with the right fist in the left palm and then you 'shot' out your right fist to the side, pushing with the left palm. From that I always remind myself that right fist covered with left palm is 'begin fight' and left fist covered with right palm is 'peace' or stop fight.
It's called Bojumeok (보주먹) in Kukkiwon Taekwondo (http://taekwon.net/mks/files/attach/images/130/859/002/d9a9a87f6fc340c73053285d96bba4f7.jpg).
As far as I understand it (and it wasn't touched on much in our Kukkiwon Master Instructor Course in Korea) it's a mainly symbolic movement, simply representing umyang (the Korean version of yin-yang, used on the Korean flag) - one hand tightly clenched representing strength and rigidity and one hand softly wrapping it representing gentleness and fluidity, both are useful in martial arts and it's knowing when to use each that is important.
there is a simple poem to remember this learned when I was very young,
"left over right , a fighter's delight" "right over left , a fight to the death" when you bow your hand placement means everything , fighters would bow showing weather is was a spar or a death match.
there are lots of meanings, but this one is being forgotten because death matches are now forbidden in most places "right over left" means only one of the fighter leaves the match alive while, "left over right" means its a practice fight, or sparing match as people call them now
Hate to burst everybody's bubble about peace and war, and all the elements and that.. but it literally means thank you. It is not limited to martial arts.. purely a common way to express gratitude.
I am an academic, so here is my evidence (in non reference format): "The gesture for thank you in Chinese is to cover one's right hand with the left, and raise them chest or head high while bowing one's head."
Link : http://survivalphrases.com/pdfs/SurvivalPhrases_Chinese_S1L01.pdf google search "Chinese thank you hand gesture"
In our Southern Shaolin tradition, the interpretation is:
Its a form of salutation, sort of like saying hello, but there are various subtleties to it. Yes the symbolism of aggression, the fist and peace, the palm is very relevant.
As is shown in the image above, with the palm wrapped over the fist, its a normal, peaceful, greeting, like a "Hello, how are you?" or shake-hands in Western culture. This is used by everybody, not just martial artists.
With a straight, open vertical palm, with the knuckles of the fist pressed against it: this is a martial (artist) salutation. It is like a bow for the Japanese. This is the common salute as adopted by WuShu, which they do before they start their performance or match.
A variation of this is with an left open palm, facing inwards and the back of a fist pressed against the palm. Because the fist is hidden, this is deemed to be more 'polite'.
Other salutes where the fist is exposed, ie: fist in front of the palm; is considered an outright challenge!
Bowing has been used thru the ages, throughout the world mostly to show subservience to your betters, to be lower than them, that you acknowledge them as your superiors. It has been adapted to show greeting salute, humility, apology and other salutations.
Many Kung fu and martial arts adapted the traditional bow to a new form to never take your eyes of your opponent. The open hand wrapped over closed fist bow was originated by a group of Quen Daoist monks from wu dang mountains. The two fists together meant battle salute while the hand covering fist meant 'I do not wish to fight but stand ready'. The monks migrated to the Shaolin temple. The Shaolin monks then edited this bow and gave new meaning to it with the left open hand. The closed fist represents the sun while the left open hand signifies the moon. The sun and the moon are the two great sources of light and when placed together they signify “Ming” which means bright in Chinese. The Ming dynasty (1368-1644) was an amazing era in Chinese history which saw an explosion in culture and prosperity. Many different martial disciplines adapted this bow and gave their own spin to it but it originated with the fathers of Gongfu not to be mistaken with the originators of martial arts which is ancient Thera 1650 bc with Minoan boxing.
As for Asian disciplines, Boddhidarma an Indian monk brought weapon styles to China and they adapted the styles to unarmed combat styles praise be Kung Fu and Karate were born but that's another topic.
Off topic: Martial discipline history is fascinating. Many styles predate any we currently practice. Japanese Koryu, German Ringen, the Togakure-Ryu manuals from India is exquisitely rich in disciplines also. I teach at Michigan state devoted my life to martial study and after 20 years barely scratched the surface