There are many holidays that are important in Mexico. I will list the three that I think are the most important. These include one secular holidays and two religious holidays.
The secular holiday falls on September 15 and 16. These two days commemorate the beginning of the Mexican wars for independence from Spain. The 15th is the anniversary of the "grito" of Miguel Hidalgo -- a call to rebellion that led to the start of the war. The war began on the 16th and that day is celebrated as Mexico's independence day. The reenactment of the grito is a big thing in Mexico -- it is reenacted all across the country on the night of the 15th.
The two religious holidays are Dia de los Muertos (day of the dead) on November 2 and the feast of the Virgin of Guadalupe on December 12. The Virgin of Guadalupe is the patron saint of Mexico and her feast day is the date on which she is supposed to have appeared (in the form of an Indian woman) to a Mexican Indian peasant in 1531.
There are many other Mexican holidays, but these are three most important in my mind.