First person perspective: Viewing the world through the eyes of the primary character in three dimensions. e.g. Doom, Quake.
Second person perspective: Viewing the game through a spectator's eyes, in two or three dimensions. Depending on the game, the main character is always in view. e.g. Super Mario Bros., Tomb Raider.
Third person perspective: a point of view which is independent of where characters or playing units are. The gaming world is viewed much as a satellite would view a battlefield. E.g. Warcraft, Command & Conquer.