Recall is an instant teleportation method available during a quest or while outside in a wilderness adventure area. It is performed via the "Recall" button on the quest objectives window.
While in a quest, you can recall and exit prematurely, without having to return to the entrance, by clicking the recall button. Once all mandatory quest objectives are met, and the quest XP is "locked in", the button will change to read "Finish"; hence the phrase "finish out", or "FO".
Recalling from inside a quest will take you to the entrance of that quest, whether that be in a wilderness or public zone. For quests whose entrances are within other quests, recalling will take you to the outermost quest entrance (though re-entry usually takes you directly to the further-in quest instance in such cases).
While in a wilderness area, recalling will teleport you to the most recently visited public area. For example, entering the Ataraxia's Haven wilderness zone from the House Deneith enclave will mean that recalling will send you back to the House Deneith port agent, provided that you have not entered the local spa in the meantime.
Teleport and similar spells allow a player to freely leave any quest or wilderness zone without having to recall.
Leaving a quest prematurely will confer a penalty to the XP awarded for completion, should you re-enter that quest instance.