There are a mix of answers already offered on this question. I would like to rebut a couple of points proffered in some of those answers. These rebuttals are made with due respect - we all have different teachers, walked different paths and have learnt different things. Please don't be offended if I have chosen to critique one of your statements.
Kata's normally don't have any 'real world' implications
That has to be one of the most incredibly wrong statements I've ever heard. Centuries ago people lived and died by their kata. Not so many people die from them these days, but their meaning and intent is still there, even if it isn't as widely understood or taught as it once was. Some kata have evolved over time, usually due to teaching styles and preferences - this is normal within martial arts (styles evolve over time). There is also anecdotal evidence that a lot of knowledge was withheld from American GI students after WWII, leaving them to decide (invent) the knowledge for themselves1.
One thing to keep in mind is that most all Kata are extremely contrived.
I'm sure there are some contrived kata/forms out there, without a doubt. However all the kata I have ever learnt were not contrived. Some of the simplest kata out there, the Taikyoku katas invented by Gichin Funakoshi, are full of death and destruction. They contain just simple blocks and punches, right? Turn left, block the kick/punch coming from that guy, turn right, block the kick/punch coming from that guy and then hit him in return2 yada yada yada yawn... If this is what you think the kata is then you have been sadly mistaught.
Katas were assembled by teachers and families, the "owners" of styles. It is a package of moves that represents their knowledge, each move could have several specific applications (bunkai). The owners of the kata would keep the meaning of them secret except to the select students who were taught them, the moves and knowledge in the kata gave them a competetive advantage over the family or school on the next farm when issues arose and fisti-cuffs started. These "owners" also didn't have dozens of katas like we do these days, they had just a few which they honed to absolute perfection.
You don't use all the moves in a kata one after the other until the opponent falls over - if you need more than one or two moves from a kata then you are doing it wrong. In some kata the third move may be the same as the first move but they are not necessarily doing the same thing. In a sequence of moves that consist of a straight punch followed by a groin block followed by another straight punch, consider this:
- taken individually, the straight punches can both be doing exactly the same thing
- the first straight punch is done followed by the groin block
- the groin block is done first followed by a straight punch
In cases 2 & 3 the straight punch can be doing something vastly different. When in a fight I can use moves 2 and 10 from the kata provided I have sufficient understanding of it to do so, I don't have to start at move 1 and progress to move 2.
Each move from a kata has specific applications. After I execute one of these moves on an opponent, I know exactly the position he is going to be in, I know where his head should be, where his torso should be, etc. If I execute the same move with my eyes shut in a pitch black cave, I still know exactly what I have just done to him and his body position. Depending on the exact application I just used, I know whether I need to follow up with something else, and depending on his (and my) body position I know which kata technique I should use next.
Even simple bunkai is powerful. Take one simple move found in many kata: soto uke while pivoting sideways into kiba dachi (inner block while pivoting sideways into horse riding stance). Depending on how I'm engaged with the opponent when I start this move it is either an arm break/elbow dislocation, a knockout, or a hip dislocation. This stuff is all buried in the kata. If successfully executed then this move is all I need to stop the fight.
Kata trains the mind and muscle memory. Every single move you execute in a kata, you should be visualising what you are doing on your opponent. As your knowledge grows you will have more options to visualise, even back in the basic kata you learnt when you were a white belt. This visualisation is what helps to cement the knowledge I talked about in my previous point, where I know exactly what I've just done and what position the opponent is in. Visualising the bunkai of the kata assists with the state of mushin, where you do not have to consciously think about your current or next move, it just flows.
1 I will try to dig out some citations to support this in the next day or two.
2 Please please please stop and ask yourself: what happened to the first guy where all you did was block his technique? Is he going to stand there and patiently wait for his next turn while you deal with his friend? Do you really believe kata are teaching you that?
3 I should point out that the Taikyoku katas are a watered down or simplified version of the Heian and Kusanku katas.