F3 is an acronym for FFF which in turn is an acronym for: "Fat Fucking Failure". Some say just "Fail" instead of the full "Failure". Used in internet slang to say that an event is bound to be/or is a failure i.e. not as good as the organizer intended.
OR
Comes from an MMORPG named MapleStory, where the F3 key would change your character's face to show a troubled look. Players use it for more of a sarcastic jesture and when they are not ingame, they would would simpyl type "f3" at the end of a sentance to indicate sarcasm.
MSN chat:
guy 1: Brb going to pierce my own tounge.
guy 2: that sounds safe F3.
guy 1: F3.