United, if at all, by a taste for shock humor and disdain for authority, this leaderless Internet hive brain is plundering and playing in the electronic networks of an ever shifting enemies list: Arab dictatorships, the Vatican, banking and entertainment firms, the FBI and CIA, the security firm Stratfor and even San Francisco's BART transport system. Did Anonymous fix the TIME 100 poll? "Depends who you think is smarter, a global collective of highly skilled hackers or the TIME IT department," says one fellow traveler, anonymously. Anonymous earned its place on the list, one way or the other.

If the above comment is confusing, sample this:

There is so much material on the internet about these elusive hacktivits, that again I will take wikipedias help to simply define what this group does.

Anonymous is a loosely associated hacktivist group. It originated in 2003 on the imageboard 4chan [that is howI got to know about them, right here The Case of Anonymity], representing the concept of many online and offline community users simultaneously existing as an anarchic, digitized global brain. It is also generally considered to be a blanket term for members of certain Internet subcultures, a way to refer to the actions of people in an environment where their actual identities are not known. It strongly opposes Internet censorship and surveillance, and has hacked various government websites. It has also targeted major security corporations. Its members can be distinguished in public by the wearing of Guy Fawkes masks. 

Anonymous has been posited by CNN to be one of the three major successors to WikiLeaks. As mentioned before, in 2012, American magazine Time named Anonymous as one of the most influential groups of people in the world.

Some of their claim to fame:

The group is responsible for cyber-attacks on the Pentagon, News Corp and has also threatened to destroy Facebook. The group gained worldwide press for Project Chanology, the protest against the Church of ScientologyIn October 2011, "Operation Darknet" was launched as an attempt to cease the activities of child porn sites accessed through hidden services in the deep web. Anonymous published in a pastebin link what it claimed were the user names of 1,589 members of Lolita City, a child porn site accessed via the Tor network. Anonymous activists merged with Occupy Wall Street protesters. Anonymous members descended on New York's Zucotti Park and organized it partly. They also claimed responsibility for taking down government websites in the UK in April 2012 in protest against government extradition and surveillance policies.

In its early form, the concept has been adopted by a decentralized online community acting anonymously in a coordinated manner, usually toward a loosely self-agreed goal, and primarily focused on entertainment. Beginning with 2008, the Anonymous collective has become increasingly associated with collaborative, international hacktivism. They undertook protests and other actions in retaliation against anti-digital piracy campaigns by motion picture and recording industry trade associations. Actions credited to "Anonymous" are undertaken by unidentified individuals who apply the Anonymous label to themselves as attribution. Some analysts have praised Anonymous as the freedom fighters of the internet,and a digital Robin Hood, although others have condemned them as "anarchic cyber-guerrillas".

Personally, they won me over with the Vendetta look [it is Alan Moore's best]. But my interest primarily lies in the meme created by these internet warriors, and the means they adopt to keep this sub-culture (?) alive & thriving. There is distinct iconography, language, manifestations, location, community behavior....and no way is this culture endangered. 

No need for link in this one. Experience their influence first hand.