The 5th of May is not, in fact, Mexico's Independence day.  Mexico declared its Independence from Spain at midnight, the 15th of September, 1810.  So what is so important about Cinco de Mayo?  On May 5th, of 1862, in the city of Pueblo Mexico, 4000 ill-equipped Mexicans surprisingly defeated a French army of 8000 strong.  This French army, under the rule of Napoleon III, had not been defeated for over 50 years.  When the battle was over, many French were killed.  This victory helped to keep Napoleon III from supplying the confederate rebels for another year, allowing the U.S. to build the best army the world had ever seen.  This superior army went on to defeat the confederates at Gettysburg just 14 months after the battle of Pueblo, putting an end to the civil war.

Battle of Pueblo