The 5th of May was the day when Mexicans who were poorly armed, defeated the French.
That day is celebrated today as a symbol of resistance. You have to understand that
Mexico previously defeated Spain in 1810, & later won against America in 1868.
So they defeated 2 major powers already & despite not having the military might,
Mexicans proved themselves formidable against France in their 3rd foreign
conflict situation to maintain their Independence as a free & strong people.

Find out more about this celebration

Here’s a More In-depth view of the history.

http://www.youtube.com/watch?v=aqUDUoMh9bo
Another Short Perspective

http://www.youtube.com/watch?v=QIICWQyK72Y
And More on why it’s popular in America.