Despite what most people think, Cinco de Mayo is not a celebration of Mexico's independance from Spain. That's September 16th. Cinco de Mayo is instead a celebration of the victory of the Mexican militia over the technologically advanced French army. It's also not celebrated as strongly in Mexico as it is in the US where Cinco de Mayo has become a day to embrace Mexican culture. I know I plan to over some kickin' enchiladas tonight!
Read more about the history of Cinco de Mayo here.