Cinco de Mayo, May 5, commemorates Mexico's victory over the French Empire at the Battle of Puebla in 1862. It is a regional holiday in Mexico (especially Puebla) and a major Mexican-American cultural celebration in the United States.
On May 5, 1862, an outnumbered Mexican army defeated invading French forces at Puebla. Although Mexico ultimately lost the war, Puebla became a symbol of resistance. The holiday is much bigger in the US than in Mexico, where it is only a regional observance.
In Puebla: military parades, battle reenactments. In the US: Mexican music (mariachi), Mexican-American food festivals, parades in cities with large Mexican-American populations (Los Angeles, Chicago, Houston, Denver).
Tacos, enchiladas, guacamole, margaritas. (In the US, often more loosely Mexican-themed than authentic.)
"Feliz Cinco de Mayo".
Not a national holiday in Mexico — businesses operate normally outside Puebla. Major celebrations in US cities with large Mexican-American communities.