A rare, fleeting experience when you come into contact with someone who you are strictly friends with on Facebook. This person may have been in that one class freshman year, or met during an evening of heavy drinking followed by a clutch friend request at 3AM. Facebook unicorn's namesake comes from the unicorn itself. You've read about it, you've seen pictures of it, but interaction in real life is strange and uncomfortable. The slight nod of the head and acknowledgment of existence is the proper response to the phenomenon, to act as if you actually knew who they were would only degrade yourself (see: creeper).
Guy 1: Hey, isn't that the chick that was in our Bio class freshman year?
Guy 2: Yeah. She's dating John Smith and has a cat named Sarah Palin.
Guy 1: Dude you're a fucking creeper.
Guy 2: No, she's just a Facebook Unicorn.