A leaderless group on the internet. Anonymous could be anyone and therefore, it is primarily split into divisions of hacktivism, lulz and protesting. The hacktivism (don't think I need to explain this) section of it is the most well known form of Anonymous, however many people do not understand that this is only a subsection of Anonymous and not the entire thing. The "Lulz" section are the people who like to... make lulz. The protesting section of it is when people protest against something (like Scientology) wearing Guy Fawkes masks to conceal their identity. The term "Moral fags" is a term to tease the people who protest and use hacking for purposes other than lulz in the Anonymous group according to the ED article (I don't advise you go there).
Anyone could be Anonymous, even you! Fox news won't like you, though.