An unusual person who likes things you put on facebook, and may or may not make you uncomfortable. If you're okay with it, then probably the term is used endearingly, otherwise it's used when full of hate. It's sort of like calling someone a tickle monster.
Stacy liked all my pictures of me and my cat
Awwh what a like monster!
Bob from work liked the picture of my cat...
Seriously?! WHAT A LIKE MONSTER.