Watching the Mayweather vs Paul fight, and even the TikTok vs YouTubers fight, I noticed they always grab each other by the head or the waist when they get close. Is this to reset the match, or even just part of a tactic?
Put simply, the clinch is a defensive tactic that is pretty effective in reducing the amount that you are being punched for a low expenditure of energy that is largely permissible in the rules. By "hugging" the opponent (and the article goes into a bit more detail of the technique of it), you're reducing their ability to punch you with any force while getting a chance to relax and regain energy. As a bonus, it tends to frustrate the opponent, and if they get angry and attempt to still throw punches, they're expending a great deal of effort to do only a little damage (their arms are weighed down by yours, the close counters means they can't get much more distance to generate force, and their only viable target is the torso rather than the head).
You are, of course, not allowed to maintain a clinch indefinitely, which is why, as you say, it tends to lead to a reset, which can also be advantageous if you were in a bad position. Lastly, if a boxer keeps clinching, it is technically against the rules, so they risk having penalties assigned, or even a judgment that they have lost the match due to being outclassed. That said, as the linked question notes, it's rare for this to be penalized in that manner.
Adding some point to very good Macaco Branco answer. Particularly about this:
grab each other by the head
Sometimes, starting with such grabbing, you may catch your opponent's glove to lower it, and then immediately hit him in this newly-created gap.
It may be called "dirty boxing" and is usually done carefully, without referree watching.