Cinco de Mayo is a holiday and significant historical day of celebration for the Chicano communities here in America. It marks the victory of the Mexican Army over the French at the Battle of Puebla.
Even though the Mexican Army was eventually defeated, the "Batalla de Puebla" came to represent a symbol of Mexican unity and nationalism. Cinco de Mayo is symbolic of Mexican Unity. It is primarily celebrated in American communities where there is a large hispanic and chicano population.
Here in the United States, the "Batalla de Puebla" came to be known as simply "5 de Mayo" and many people have equated this with Independence Day which it is not. Mexican Independence Day is a Mexican Federal Holiday and it is on September 16th.
Cinco De Mayo is not a national holiday in Mexico although it is another excuse to fiesta. It's not a big deal. Mostly people ignore this day, business and banks and the federal government operate as normal. Although it is regionally celebrated in Puebla to some degree.