To follow and/or spy on someone you have feelings for. Those feelings need not be of a kind and loving nature. People who stalk are usually obsessed with the stalkee.
Dude One: I think that girl is stalking me man and it's freaking me out.
Dude Two: Oh man don't sweat it. It just means you're in love!
Dude One: Okay seriously man, what the fuck?