Usually used in internet chatrooms when someone is pretending to be away from the keyboard, also known as lurking.
They will not respond to any messages you send to them, they are only there to be entertained.
That girl was fafk so she could eavesdrop on the quarrel without getting involved.
When someone is in a chatroom, or a messenger program when they just stop responding. Usually they have an awkward conversation and it's their attempt to avoid it. Other times they went to the restroom or to do something really quick.
Vagiquita: How you doing girl?
Shaniqua: Great, just watching tv.
Vagiguita: I heard about the new guy in your life, how is he? His names Nahoejay right?
Vagiquita: Shanni? You there?
Vagiquita: Bitch you went FAFK I know you're there...