It's not the Mexican Independence Day (that's September 16); it has nothing to do with a common sandwich spread, and it is celebrated more widely (and more wildly) in the United States than in Mexico. So what exactly does Cinco de Mayo mean, and why is it celebrated?
It boils down to a celebration of courage in the face of overwhelming odds. I don't have to be of Mexican descent to find that worthy of a celebration.
Here's a great article that gives all the details of this heroic day in Mexican history.