Often abbreviated as "Anon", Anonymous refers to an indefinite collective centered around the chans. This group of internet users communicates without consistent usernames on various chans. Between posting gore and porn threads, Anonymous stages largely unsuccessful raids on other websites. Originally, the idea of Anonymous was to act as a hive mind as part of a meme. Enchanted with anarchy and convinced they were part of some Internet Fight Club, 13 year olds everywhere took the idea of a faceless force of nature to heart. These diehards became convinced that Anonymous could enact real change, and the meme degraded into what is often referred to as "legionfaggotry" by /b/tards.
In the old days of /b/, not many people took Anonymous seriously, and they treated it like the joke that it was. Anonymous was more of a subculture than a definite group, a loose community where nobody had a name and were content to talk about random things and occasionally organize trolling attempts on other sites. This changed when FOX 11 decided to report on the trolls, and true legionfaggotry started to take hold. Some users took to writing up eloquent speeches about how much these guys they knew on the internet rocked. They romanticized Anonymous as a force of total nihilism or an unstoppable anarchic villain, when in reality it was closer to a group of disillusioned men and teenagers meeting up on the internet in flash mobs where they would either waste time or insult people who knew less about the internet than them.
Because Anonymous is in essence a collective, ongoing flash mob, there's no true hierarchy or organizational structure. The only real "rule" seems to be the understanding that messing with cats is crossing the line. Because there's strength in numbers, especially numbers that include effective trolls, Anonymous isn't a completely powerless mass of offensive and frustrated teenagers. However, continual disorganization and general incompetence ensures that Anonymous will never be an invincible internet powerhouse, and only as influential as any mob can be.
It should be noted that 4chan is one of the few chans that still openly embraces Anonymous. Even so, with the exception of /b/, the boards are much less sympathetic to calls for raiding and trolling than in the past, and some even ignore Anonymous outright. The rest of the chans try to separate themselves from Anonymous, and often take measures regarding the name field to do so.
Anon Anonymous actually started out in 1993 with the launching of anon.penet.fi by Johan "Julf" Helsingius of Finland. An anonymous remailer whose members ran into the hundreds of thousands. Making it the very first and original Anonymous! It would strip technical information and than send messages to Usenet Groups. Many notable trolls were counted amongst its users.
However, today's Anonymous grew out of the "tripfag debates" on 4chan. In 4chan's early days, using a tripcode and pseudonym wasn't just accepted, it was encouraged. Moderator Shii, who had some experience with 2ch wrote an essay on why this totally sucked, and moot made him a moderator because of it. Shii, as soon as he gained his staff powers, eliminated the name field on many of the boards, implementing forced anonymity. People who used tripcodes whined about the new forced_anon and began signing their posts with their old names, inviting ridicule from those who welcomed the changes. Regularly, there would by "tripfag vs anon" threads where the tripcode lovers would accuse the people who didn't use names of being a single person or hive mind. As such, Anon was every 4chan user who had ever posted on the boards. The meme continued to grow in popularity until it blew itself out of proportion and into the fragmented mess it is today.
Eventually a FOX 11 report aired which described Anonymous and 4chan as an "internet hate machine" and as "domestic terrorists". This caught on rather fast with the boards, leading to memes mocking the poorly researched report. However, at this point, Anonymous grew into something more serious as the users romanticized Anon into an anarchist group of Joker-like characters that were the mass subconsciousness. This lead to Anonymous first "project" called Project Chanology, which was a broad attack against the Church of Scientology.
And from there, Anonymous became more "organized" (or as organized as a mob can be) into an activist group interested in protecting the "public welfare", which can range from helping Wikileaks to simpler goals like catching a cat killer. But at it's very core, Anonymous is still essentially a group of hacker trolls with loftier and more "noble" goals than simple trolling.
Anonymous, though largely toothless, still contains people with sufficient hacking and trolling prowess locked away in its tightest regions, most of them solely focused on the Wikileaks drama. Despite this, Anon does largely seem to fall back on hackneyed "troll" tactics like doxing opponents, and then making death threats on their lives and family through email or the phone. It also occasionally uses DDoS attacks if their opponent has a website, but it still stands that Anonymous is more bark and less bite.
In the last few years, 4chan has become more mainstream and most posts are of the paint-by-numbers, insert-meme-here type, with less and less people supporting Anonymous then there used to be. This has lead "legitimate" Anonymous members to take up residence on other *chan boards as well as IRC networks such as AnonOps. This has lead to splinter groups like LulzSec who attempt to invoke their own "hacktivist" ideals, but largely failing due to a lack of social skills.
Anonymous people don't say "Gentlemen" - they say "Anonymen"
L is Anonymous.
Logo for the BfV of Germany
Fox News logo
Image used for telepathy proxy Rebecca Bue Li in White Wolf's 1997 RPG Trinity. http://whitewolf.wikia.com/wiki/Trinity
From V For Vendetta