Mexican War of Independence
The Mexican War of Independence () was an armed conflict, and the culmination of a political and social process which ended the rule of Spain in 1821 in the territory of New Spain. The war had its antecedent in Napoleon's French invasion of Spain in 1808; it extended from the Cry of Dolores by Father Miguel Hidalgo y Costilla on September 16, 1810, to the entrance of the Army of the Three Guarantees led by Agustín de Iturbide to Mexico City on September 27, 1821. September 16 is celebrated as Mexican Independence Day.
Puebla
Cinco de Mayo—or the fifth of May—is a holiday that celebrates the date of the Mexican army's 1862 victory over France at the Battle of Puebla during the Franco-Mexican War (1861-1867). A relatively minor holiday in Mexico, in the United States Cinco de Mayo has evolved into a commemoration of Mexican culture and heritage, particularly in areas with large Mexican-American populations. 
Many Americans mistakenly believe that Cinco de Mayo (“May 5th”) is the Mexican equivalent of the United States’ Fourth of July holiday — a date marking the official casting off of colonial rule via the announcement of a new independent country. However, the Mexican version of Independence Day is celebrated on September 16, for it was on that date in 1810 that the commencement of the war for Mexican independence from Spanish rule was pronounced in the small town of Dolores by Miguel Hidalgo y Costilla (an event now referred to as the “Grito de Dolores” — “Cry of Dolores” — or “El Grito de la Independencia”).