A player's mettle isn't tested solely by his or her ability to press buttons in the right way, at the right time. When playing against another person, skill is only part of the performance—nevermind when playing with an audience present.
Pressure is a real thing, and smart opponents will try to psyche you out however they can. Or, they might try to rile you up, humiliate you or prove their dominance somehow. This is where taunting comes in.
Taunting is a huge part of competitive play, so much so that people find ways to do it even when a game doesn't provide you with one. See, most notably: teabagging in just about any game that allows you to crouch. Alternatively, more polite players might do an action over and over again (like meleeing) just to give you something to look at during the kill cam. Whatever sends the message across.
Street Fighter
Perhaps the most famous in-game taunting would have to be for fighting games. Sometimes, these taunts relay simple messages that are the equivalent to ‘come at me, bro.' Sometimes, they're just folks showing off. And my personal favorite—Dan from Street Fighter, a character whose entire existence is pretty much that of a joke character. He has a giant goofy grin, a pink gi, and some of the best taunts in any game.
When a player busts out Dan, you know that they're doing it for kicks or so that a potential win feels like a knife twist—because in that case, you didn't just lose. You lost to Dan.
Here you see Dan starting off with a move that's literally called "Legendary Taunt," which is silly by itself, but then it's comboed into an ultra, which, yes, also looks absurd-and then ends with a taunt! Perhaps most hilarious is that one of Dan's normal taunts can be used to cancel some ultras for added embarrassment... or that Dan is surprisingly capable in battle.
What Dan here represents is my favorite type of taunt: the useable taunt. It's not just for show; you're not just pressing a button to do something cool.
Team Fortress 2
Think, for instance, of the taunts in Team Fortress 2, which can one-hit-KO an enemy if done correctly—like the scout's baseball taunt. The timing on this taunt is tricky to keep the game balanced. If you're not careful, the move could actually put you in danger. But if you do manage to land the taunt, then not only do you get the satisfaction of pulling it off, you get a kill and your victim likely feels humiliated. Score.
Gears of War
Other programmed taunts don't come in until after an opponent's death. In Gears of War 3, you have the ability to execute a player and, for extra points, to keep that execution going for far longer than it has to. You might, for instance, rip someone's arm off and them beat them with it for a while. The player can't respawn while you do this, they have to suffer through their disgrace.
It's difficult not to resort to these taunts even when you know they'll get you killed, because they're just that satisfying to do depending on the game. In this case, Gears features rivals, which a match denotes after someone kills you at least five times in a single match. Rivals are perfect excuse opportunities to taunt.
It's surprising that for such a bro game, there are no bro taunts in Gears of War, though. They're practically the most important kind of taunt!
Mortal Kombat
Though typically not identified as a taunt, I don't know what else you'd call the fatalities in Mortal Kombat. If a taunt's purpose is to "anger, wound, or provoke someone" (according to the dictionary), that's exactly what the gruesome act against a dazed, nearly dead opponent does... which is to say, not all taunts in games are identified as such.
When it comes to fatalities, they're like the final sendoff—only, it isn't just about letting you die, it's making sure you die in the most vicious, ‘scenic' way possible. It's super aggressive.
I never was able to pull off a damned fatality—and that just made me feel that much more inferior when they happened to me.
A lot of what taunts boil down to, then, is power dynamics. You're showing someone you're capable and powerful, you're proving that you're in control of the situation, that you overwhelmed them, or that you have the confidence to be reckless. Taunting is almost always reckless, after all.
Even when it's a ‘for fun' thing, when you're just being silly, it's still a power dynamic. You're essentially saying that you have the freedom to not take things seriously, which can be particularly provoking for someone.
A lot of what taunts boil down to, then, is power dynamics.
It's strange to think, though, that some of these examples—programmed examples!—arguably go kind of far. Taking a whole minute of subjecting someone to a taunt would probably be considered bad sportsmanship in real life, no?
In a video game, though, it's just another challenge for a player, another thing that tests them—it's just a part of the competitive spirit.