PvP

Player versus player, or PvP, is a type of combat in MMORPGs, MUDs and other computer role-playing games pitting a player's skill against another's, where the goal is ultimately the death of the opponent's player character. While this can include player killing or PKing, this term is usually used in a narrower sense. It is the antithesis of combating mobs, known as player versus monster (PvM) or player versus environment (PvE).

For the complete Wikipedia article on PvP see here.