In 1861 the French decided to use the fact that Mexico had declared a moratorium on its debts as an excuse to invade. However, in 1862 an outgunned Mexican army won a lopsided victory over the French near the city of Puebla, about an hour's drive east of Mexico City. The holiday of Cinco de Mayo commemorates that victory. Unfortunately, about a year later the French attacked again and prevailed, installing Maximilian of Hapsburg as Emperor where he remained until he was executed in 1867. Mayo is not considered a particularly important holiday.
People are happy for the time off but that's about it.
It certainly does not generate nearly the hype that it does in this country where it has been mercilessly promoted as a celebration of Mexico and its people by the Mexican food, drink and restaurant industry. Frankly I don't see anything wrong with this. Mexico and Mexicans certainly deserve to be celebrated, and, for those who need an excuse, the fifth of May is as good a time as any. There is great dispute over who invented the Margarita. But unless you or someone close to you is one of the pretenders the truth is probably not important.