1. Someone who is hiding their identity (the original definition)
2. A hacktivism/real-world protest group comprised of, well, really anyone that wants to be an anon. Large and decentralized, they originated on 4chan and the like. They then went after scientology, and now they are after those who oppose free speech. They have been largely hated upon by people who don't understand anything about them, and cannot be bothered to do some research. Somehow they are also blamed for anything any hacker does, even though that is like hating fruit because you happened to get the one rotten fruit in the whole store. They are like any other big group that gets a lot of attention: at the core, there are people who really do care about what they say they do, and either use the internet or real protests to help their cause, BUT, there are also idiot children (either literally or at heart, and not in the good way) who use the group to get attention. (usually identified by "wE tyP LyK dIS!") This happens to every group or organization that gets attention. Stop hating, just go outside or read something else.
Fred: I hate anonymous, they're a bunch of fags!
Room: Yes, Fred, we know. You also hate gays, jews, and fruit. stfu.
George: I got hacked! They stole my e-mail, password, and they're after my money! SCREW YOU ANONYMOUS!
Mike: Dude, you clicked on the FR33 p0rN!!!1!!!55566 e-mail. That's not Anonymous, that's your fault, retard.
Anon1: Man, I love protesting legally on the streets and taking down websites with no security to speak of for a good cause.
Anon2: I know, right!? It's also hilarious how pissed people get because they can't do a single thing about us!!