In many PC, console and table top rpg games, the Player Character is under the control of human players as opposed to the game's AI or a human dungeon master (called NPC's (Non-Player Characters) or simply monsters, depending on the nature of the game).
The wide variety of games that use this concept (almost all of them) makes it difficult to place anything other than a general description on the topic, however all PC's have this much in common.
Names
Player Characters are always almost named, and it is rare to have play a game where the protagonist is named "guard" or "solider" (although there are a handful of Console role-playing games that briefly use generic names for player characters). Console RPG's are also notorious for having a limited number of character spaces for names.
Statistics
Ranging hugely from some loose descriptions and some numbers indicating strength and magic power (e.g. Diablo and Dungeon Siege) to hugely complex multi-screen systems detailing extensive character strengths and weaknesses (Baldur's Gate series and Deus Ex). From these screens characters' equipment and inventory can be viewed and changed. Point and click style games generally offer a static PC for the player to use, though the inventory is all-important in this style of game.