The clue is in the name.
All sort of hacktivist groups, or just plain tossbags who like associating themselves with the cachet, claim to be anon.
Actually, anyone can be. Just join up to a cause without revealing your identity; in the original case, the homebase was the chans (primarily, but not exclusively 4chan /b/ forum) because they allowed fully anonymous posting. No username was required to make or reply to a discussion or image thread, and because of the speed that things moved on that forum, even if logs were kept, they were of little use because threads tended to get auto-wiped because of either size or age after maybe a couple of days tops. One imagines the server logs rapidly went the same way. Any subpoena for them would be met with a "sorry, but we ran out of space, and everything older than a week has already been erased".
It was also supposed to be a bit like fight club. You don't talk about it outside of /b/. You certainly don't claim membership. Even though I only ever really lurked when on such sites (i've given up going; massive time-sinks for little payback...), I've still had to chew out a younger friend who thought they were so hip and edgy by going on about /b/ and anonymous all the time... Really, anyone who doesn't "get it" and checks out what you're talking about will think you're either sick, or a douchebag; anyone who DOES, almost certainly already knows about it, and knows about The Rules... and therefore thinks you're a DB.
They are faceless, legion, and entirely random. Not anyone's private army. If they take a stance against something, it's either because they have collectively been offended by said thing (e.g. Scientology), hating on it has become a meme, or just think it's amusing to do so. All three things tend to blur into each other. For the lulz, as it were.
Also, plausible deniability, and being able to evade vicitimisation by potentially corrupt authorities, is a very powerful tool in the fight for justice and democracy. You don't have to hide forever, and it can be damaging if you want to still remain anon when things reach a legistlative rather than protest stage, but in the early days it can be a very sensible idea.
