It celebrates the Battle of Puebla, when the Mexicans kicked some French ass.
Incidentally, it was also the day Napoleon died, which prompted Alessandro Manzoni to write a massive Ode to the great men.
Italian kids are usually forced to learn it by heart at school: if you want to force flashback on a bunch of unsuspecting Italians just shout at the top of your lungs "Ei fu, siccome immobile !" - they will not be able to resist, in this respect we are much like the cartoon characters in the Who framed Roger Rabbit movie.