Cinco de Mayo is Spanish for "fifth of May". It commemorates the triumph of a small Mexican army over French forces in an 1862 battle.
Although the Mexicans did not win their war, they continued to fight for the next five years before expelling the French in 1867. It was an inspirational example of how the Mexicans were strong enough to fight against all odds.
In the United States the date celebrates the culture of Mexican ancestry, much like we celebrate St. Patrick's Day, Oktoberfest, Kwanzaa and the Chinese New Year.