Gang-stalking is an imaginary phenomenon suffered by absolutely no one but propagated by paranoid schizophrenics on the Internet who use the groupthink reinforcement of web communities to support their delusions. It's the belief that one is being followed constantly by others as part of some kind of government of shadow organization plot; the unfortunate mentally ill people who believe in it have developed an entire lexicon of terms like "targeted individual" (which you'll see in several definitions here) to describe and rationalize their paranoia.
People who believe they're being gang-stalked read patterns and conspiracies into absolutely everything. A fellow shopper looks at them funny (probably because they were acting visibly crazy)? Gang stalker! Misplaced car keys? Gang stalker! Get a lot of junk mail one day? Gang stalker! Neighbor make noise while taking out their trash? Gang stalker!
If you ever want an awkward, schadenfreude-induced laugh, Google "gang stalking" and read some of the stories. These people deserve pity more than scorn, but holy shit they're fucking crazy. They're so desperate to believe they're being "targeted" for being "free thinkers" or "dissenters" (read: they browse conspiracy theory web sites and have convinced themselves someone is tracking them). The reality - that they're just mentally ill and no one cares enough to get them help, let alone to organize gang stalking efforts against them - is too bleak and depressing for them to acknowledge.
My batshit crazy downstairs neighbor believes she is suffering from "gang stalking" because she is severely mentally ill. She opens her door and screams at no one with accusations including: "you" are stealing her shoes and cutting them so she falls down when she walks; "you" follow her when she goes grocery shopping; "you" made tiny nicks in her windshield wiper blades; "you" have the police on your side because they won't believe her when she calls them.