Atheist's Day is a day to celebrate atheism and unite people in the understanding that just because you do not believe in a deity doesn't make you a bad person. Atheists tend to be good-natured and open-minded people who celebrate realism, scientific proof, and life.
This day became known from a prank that was posted on April Fools Day that involved a fictional case of an Atheist suing the government because, unlike other religions, there was no day for Atheists. The judge threw it out saying April 1st (April Fool's Day) is the Atheists' Holiday since the bible verse "The fool hath said in his heart, there is no God" - Psalms 14:1, claims that atheists are fools and that this is their day.
Whoever started that post or created the rumor of the post, started a holiday that was embraced by the Atheist community and has become wide spread. This is the day to raise awareness to the growing number of atheists in our society.