Despite what some people inaccurately think, Cinco de Mayo does not mark Mexican Independence Day (that would be Sept. 16). The holiday, rather, commemorates the 1862 battle of Puebla that Mexico fought and won against the advancing French army, led by Emperor Napoleon III. Mexico was still occupied by the French a year later, but the Puebla victory came to symbolize unity and pride for what seemed like a Mexican David defeating a French Goliath. Today the holiday is celebrated in the town of Puebla, but it's not an obligatory holiday in the country.
Still, that doesn't really explain why the day is so popular in the U.S. Cinco de Mayo started to come into vogue in 1940s America during the rise of the Chicano movement. And much like every other holiday in existence, it became commercialized in this case, by the alcohol companies trying to tap into the Hispanic market. Thus was born a day of drinking tequila while wearing a stereotypical sombrero. So much for supporting Mexican pride and nationalism.