Anonymous is what it's called when someone does something but doesn't want to be identified. This could for example be a poem or a charitable donation.
"I have lots of promiscuous sex with someone other than my wife."- Anonymous
Notice, the person who penned this wishes to remain anonymous, that is, he is wishing to not be identified.
Let's take a look what would happen if the person identified himself.
"I have lots of promiscuous sex with someone other than my wife"- Ted Haggard
If Ted Haggard announces this to the world, he will lose his job as leader of the mega-church.
Of course, here is another example, to end on a good note.