My avatar:

Represents atheism. The people that made the image have released it for free publishing, so long as it represents atheism.

It is a fusion between the mathematical void symbol and the stylized representation of an unicorn.

The void symbol (empty set ?) is an allusion to nothingness and in this case meaning "no faith" or "no god".

The unicorn is a reference to a kind of story that atheists often tell to make their point. In this case one of the first stories to circulate the Internet newsgroups: The Invisible Pink Unicorn.

If you want to know more about the story of the Invisible Pink Unicorn, for purposes of demonstration:

"The Invisible Pink Unicorn (IPU) is the goddess of a satiric parody religion aimed at theistic beliefs, which takes the form of a unicorn that is paradoxically both invisible and pink. These attributes serve to satirize the apparent contradictions in properties which some attribute to a theistic God."

"The IPU is commonly used to highlight the perceived fallacious or arbitrary nature of supernatural beliefs by, for example, replacing the word "God" in any theistic statement with "Invisible Pink Unicorn". A quote from the alt.atheism FAQ sums up this use of the Invisible Pink Unicorn:"

"The point of this silliness is to prod the theist into remembering that their preaching is likely to be viewed by atheists as having all the credibility and seriousness of [the atheists'] preaching about the IPU."