The origin of any kind of cinco de Mayo celebration starts in 1862. In 1861, the French began invading Mexico. On May 5, 1862 an 8,000 strong French army, that was extremely well equipped, was badly beaten by a poorly equipped Mexican army of around 4,000, in the state of Puebla.
The area celebrated the French loss, but over a year later France had conquered Mexico City and established Maximilian I as Emperor of Mexico. Though in 1867 Mexico ousted Maximilian and had him executed. Mexico once was again free.
Yet cinco de Mayo had spread. Mexican immigrants in California celebrated it, and continued to do so every year. In the 1940s the Chicano movement helped spread it further across the US, and the civil rights movements in the 50s and 60s did so as well. Then in the 1980s beer companies started capitalizing on the celebration and it became instituted as an American drinking holiday.
Since then it has grown bigger each year, and spread internationally. Tis now one of the top drinking days in the US, and almost comparable to St. Patrick's Day. On cinco de Mayo, most Americans celebrate being Mexican, or at least drinking Mexican beers, even if in Mexico it is just another day.