Well, if you consider offering an alternative side to theism a purpose, then I guess it does have a purpose (in that sense).
But in terms of a specific way to live, a book to follow, a doctrine to follow, or commandments to follow, there is no inherent purpose in atheism. There is nothing that guides us toward a place to worship or a way to follow.
Here is the MOS atheism definition I've put forth a few times:
atheist: "a" - without or lack of belief
"theist" - a person who believes in god(s)
"atheist" - a person that is without or has a lack of belief in god(s)
The term "atheist" is almost deemed unnecessary by the atheist community as a "non-theist" feels equally as ridiculous as a "non-gardener" or "non-chef". Since we don't refer to those things in that that way we don't need the term "atheist". Typically we only define the affirmative position on things.
The atheist proposition is that they aren't required to prove or disprove anything as it pertains to theism. They place the burden of proof on the theist who makes the initial and/or affirmative claim.
All atheism represents is a lack of belief in God or gods due to the rejection of all available evidence. Further claims of insufficient evidence (in spite of their presuppositions) or a claim of a "total lack of any evidence whatsoever" (this statement often peppered with references to "flying spaghetti monsters", "storybooks written by ancient goat herders", "fairytales", "how did Noah get every species in the ark" and "the man in the clouds") is par for the course in this type of "discourse".
Some atheists go a step further claiming that all people are atheists. Given that theists believe in their God and reject all other gods they are deemed atheists towards all other gods (this is nonsense of course, but I note it regardless).
The active portion of atheism is two-fold: one, challenging theists on their beliefs; two, keeping religion out of non-religious institutions, groups, organizations, governments, etc....
The first part of that two-fold activity is really limited to a smaller sect of atheism (the "Dawkinsian atheists" primarily....the "mock them, ridicule them" stuff) so I'd say the second portion is the primary activity (more political in nature).
Just my opinion based on my what I've experienced.
