Stands for 'Fuck and Forget', a brief sexual encounter which is purely about the sex without any feelings for the person, desire to see them again or guilt at sending them on their way once gratification has been acquired. Usually, there is only one encounter between any given set of partners. Can apply to any given encounter without regard to sexual orientation. Similar to the type of transaction one might have with a whore, only no money is exchanged. Can be used to describe someone you'd like to screw solely for the sex, but would never want to see again.
Jane walks up to Steve, wondering why Steve wont call her back after that night of hot, passionate fornication: "Bitch, you were an FAF, get over it. I've already had three since you, you're yesterday's screw. Sorry." replies Steve.