I grew up in Southern California, and as the years went by, more and more people celebrated Cinco de Mayo, or the Fifth of May, as it is translated. I used to think it had something to do with Mexico's independence, but evidently it does not, and there is another day in September to celebrate that.
Cinco de Mayo is celebrating a big battle won, where Mexico's Militia beat out the French in the city of Puebla. Many large Mexican cities have adopted the celebration and it has spread to many cities in the US also, with high Mexican populations.
I have seen them have parades, parties, barbecues, you name it.
It was an important victory because it had been a hard, long and bloody war fought for independence from Spain. France and other countries caused a massive depression, and France was hoping to gain more territories, etc. So it was a big win. That is the nutshell version.