When you first start playing the game, you create a character for yourself, and you play the game as that character.
Also referred to as just a player or a character.
Some other names used:
NOTE: Player characters are just one type of in-game character; see Non-Player characters (NPCs).
Fighting another player character is called Player versus Player (PvP).
In many role-playing games, a strict division is made between the player (the human being that plays the game) and the fictitious character that the player controls in the game (i.e., the player character or short: character). However, in World of Warcraft and its associated official internet sites, this distinction is not strictly made. Tooltips and other texts refer to the fictitous player character as "the player", thus blurring the line between player and player character. Whether Blizzard does this intentionally (e.g. to increase identification with the game world) or not is unknown.