Cinco de Mayo

It isn’t Mexico’s Independence Day!

That's a common misconception. Mexico celebrates its independence on September 16, because it was on that day in 1810 that Father Miguel Hidalgo took to his pulpit in the village church of the town of Dolores and invited his flock to take up arms and join him in overthrowing Spanish tyranny.
Independence Day is a very important holiday in Mexico and not to be confused with Cinco de Mayo.

Cinco de Mayo is a big deal in Puebla, where the famous battle took place but it really isn't as important as most people think.
September 16, Independence Day, is a much more important holiday in Mexico.
For some reason, Cinco de Mayo is celebrated more in the United States of America, by Mexicans and Americans alike, than it is in Mexico.
One theory for why it is more popular in the USA is that at one time, it was celebrated in all of Mexico and by Mexicans living in former Mexican territories such as Texas and California.  
(MY opinion: it's an excuse to party)
It was ignored in Mexico after a while but still celebrated north of the border, which never got out of the habit of remembering the famous battle.

In Puebla and in many USA cities with large Mexican populations, there are parades, dancing and festivals. Traditional Mexican food is often served or sold. Mariachi bands fill town squares, and a lot of Dos Equis and Corona (Mexican brand) beers are served.  
It’s a fun holiday, really more about celebrating the Mexican way of life than about remembering a battle which happened 150 years ago. It is sometimes referred to as a “Mexican St. Patrick’s Day.”
In the USA, schoolchildren do units on the holiday, decorate their classrooms and try their hand at cooking some basic Mexican foods.