Most will tell you its the celebration of defeating the French Army, or to hear them tell it "The great European army." Now I've always thought defeat meant to beat or win, in this case it means to delay an inevitable loss.
From what I've read at
http://www.inside-mexico.com/featurecinco.htm Some stooge tried to take the city called Puebla with a bunch of poorly equipped Indians and got their butts spanked and went home. Then when a real general and the French Foreign Legion returned 3 days later they cleaned house.
This is why they don't do much celebrating Cinco De Mayo in Mexico. Here its just another reason to party.
Thats why I say its sounds like our Alamo to me only we don't celebrate our lost battles. They say Cinco De Mayo represents when they stood up to the mighty European army and lost. Much like how the defenders of the Alamo stood up to the Large Mexican Army and was defeated. For us we use the cry "remember the Alamo" to represent when a few brave soles stood up to unsurmountable odds knowing they would die and did their best.
For Mexicans it means the same thing they just would rather call it a celebration and another reason to party