Player versus environment, (or PvE, sometimes player versus monster, or PvM), is a gameplay distinction, in contrast with player versus player (short: PvP) gameplay.
Player versus Environment is a type of gameplay common to RPGs in general. This is where the character engages in combat with AI-controlled computerized opponents, as opposed to PvP, where she/he/it engages with human players as opponents.
In Guild Wars, PvE content is available to roleplaying characters. However, a PvP character can engage a set of computer controlled opponents known as the Zaishen (especially during tutorials) as well as other players. In PvE gameplay, your primary purpose is to "grow" your character, gain experience, learn skills, acquire better weapons and armor, etc. This is done mainly by completing quests and missions, and by venturing into explorable areas to fight monsters.