A FirstPersonShooter is a game in which you see the world through the eyes of your character and shoot at (almost) everything that moves. Examples include Doom, Quake, Doom3 etc. Compare third-person (Tomb Raider, Max Payne) etc where you see the character from another observer's view, ie a camera above and behind the main character.
See GamingOnLinux.
5 pages link to FirstPersonShooter: