Quitting means a party member decides to leave the party usually against the collective desire of the party.
Players quit for a number of reasons. To name a common few: arguments with other players; being invited to a party for the wrong task (e.g. a different quest); being kidnapped. The most nefarious form of quitting is nabbing, when a player joins a party seeking a rare item or skill cap and as soon as he/she gets their item/skill, they quit. Examples of this include players farming for unique items and Ecto as well as player capping elites at Ember Light Camp.
Players can quit by simply closing the game, logging out, or by using map travel to go to any town. There is always the possibility of the Guild Wars client or the computer crashing, of course, such as with the infamous Err no 7.