Cinco de Mayo (celebrated on May the 5th) celebrates the anniversery of Mexico defeating the French at the Battle of Puebla in 1862. It has become increasingly popular in the United States as well as Mexico, and is now considered a celebration of Mexican culture.
Dia de los Muertos (Day of the Dead) is celbrated November 1st through November 2nd. It is a celebration that honors the dead, where its participants set up Ofrendas, make offerings, and party all in the name of loved ones they have lost.
Mexican Independence Day, celebrated September 16th, is considered one of Mexicos most important holidays. It celebrates the end of an 11 year war with Spain, where Mexico won their indepencence. Like in the US, it is celebrated by throwing large parties and firing fireworks into the sky.