Mexican Independence day is the 16th of September, not the 5th of May as some think. It marks the beginning of a long, often chaotic armed struggle for Mexico's independence from Spain. It lasted from 16 September 1810--27 September 1821. The 16th is marked by the "Grito de Dolores", named for the rallying cry by the priest Miguel Hidalgo in the city of Dolores in the state of Guanajuato on that day in 1810. The city, now called Dolores Hidalgo, is known at the Cuna de la Independencia, the Birthplace of Independence. Father Hidalgo was executed the following year.
Nowadays there is a huge celebration at midnight on the eve of the 16th in the main square of Mexico City, el "Zócalo," when the president of Mexico comes out on the balcony and cries, "Viva México" three times, echoed by the multitudes every time. Then fireworks and other festivities continue for hours. You can find videos on YouTube. Wikipedia has a pretty good summary of the situation both in Spain and Mexico leading up to Independence. Many other Spanish possessions of the time also gained their independence in 1821-22.
