What does it mean, when someone becomes a 粉丝 of me?

It's fanpop's equivalent of a friend request.

depends on the user
some just obsessed of getting 更多 number of fans
some wants to be friends
some add after seeing that 你 both have lots in common
some just add 你 and never get back 哈哈

Nothing. Everything will seem meaningless when we are in control! All your mortal 粉丝 will be irrelevant compared to the 海豚 Council and their great rule! I'm kidding. It means potato.