Evidently, it’s only celebrated by Mexican illegals and open borders/amnesty advocates in the U.S.
The history: Mexico defaulted on a loan from France. France invaded to enforce collection of payments and initially fought the Mexican army at a town called Puebla on May 5, 1862. http://countrystudies.us/mexico/21.htm
The region of Puebla is pretty much the only Mexican state that recognizes the date. Oh, and by the way, the French came back a few days later and kicked their ass.
The French attacked the Mexican army at Orizaba, Veracruz, on 14 June. More French troops arrived on 21 September, and General Bazaine arrived with more reinforcements on 16 October. Tampico, Tamaulipas, was occupied by the army of France on 23 October, with Xalapa, Veracruz, taken peacefully on 12 December. The French marched into Mexico City on 7 June 1863, completing the takeover. (http://en.wikipedia.org/wiki/French_intervention_in_Mexico)
The only excuse to ‘celebrate’ the temporary victory over French troops is to protest against the enforcement of U.S. sovereignty laws and accuse America of being “racist”.