Short for FaceBook Instant Message - to give or receive an instant message using facebook's chatting applet.
"So you thought s/he was cute; did you FBIM her/him?"
Gah I hate it when someone FBIMs me when I'm trying to tag photos! Facebook always crashes when that happens.
stands for "Facebook instant message". It is a way of saying that u IMed someone on facebook with the bottom chat bar, but to avoid the confusion of them thinking that you used another thing other than facebook, like AIM or Ichat, to message the person.
Bob: WTF dude. i FBIM u yesterday and u logged off!
Dylan: oh sorry i didnt get it and i was leaving to work anyways