Anonymous is word used to describe a group of people who unite under a single goal (usually connected to human rights or freedom of speech, with occasional goals "for the lulz"), do not reveal their identity and understand that in Anonymous identity is not important, and use a Guy Fawkes mask or a headless suit as their symbol. The use of these logos exclusively is done in order to show that Anonymous can be found all over the world.
Most groups that call themselves Anonymous are peaceful, but some groups are "hacktivists" that use more extreme measures to achieve their goal. In order to differentiate between the types of groups, please refer to and research the Operation, in other words the goal, they say they are part of.
Many Anonymous members are preparing to take part in Operation Onslaught on the 30th of July, as Phase One of The Plan.
Recently, 14 people from Anonymous were arrested in connection to Operation Payback, a successful attempt to DDoS several major credit card companies after they cut off financial ties with WikiLeaks.