This concept represents the in-game character controlled by the player—as opposed to Non Player Characters who aren't. Typically the game puts you in charge of at least one entity, but the extent to which that entity is an actual character, as opposed to being a Featureless Protagonist or Non-Entity General, depends on the genre, the game, the game's developers, and even (if Character Customization is available) the player him- or herself.
Sometimes, the term PC only refers to The Protagonist, particularly if they are created by the player, while NPC is used even for other party members who the player still controls but are preexisting characters within the game world, rather than a personal avatar.
It's a curious thing, but most PCs in tabletop RPGs have a sort of personality archetype that applies regardless of the genre of the game the PCs are in or the personalities of the people playing them. They tend to be:
- Sociopathic, only caring about what benefits the party (or in some cases, just themselves)
- Self-important, often striding into the spotlight regardless of how appropriate that would be to the situation they're in
- Unpredictable, constantly frustrating or amazing the GM with tricks and strategies that nobody could have anticipated
- Crazy Awesome; due to the nature of such games, PCs tend to either succeed magnificently or fail spectacularly
Finally, a wise word to all tropers: don't conflate Player Characters with players. Ryu punches Ken, Ryu does not punch the player. Unless something has gone horribly wrong. Or something has gone horribly wrong.