Cinco de Mayo: What are we really celebrating?

Cinco de Mayo: What are we really celebrating? Yesterday, Star Wars fans celebrated what everyone’s Facebook feed unofficially called “Star Wars Day” and everyone uttered “May the Fourth be with you.”  Today, many Americans will be shouting “Feliz Cinco de Mayo” and “Happy Mexican Independence Day” while many others (yours truly) will be exclaiming “Happy historical day that my ancestors defeated the French!”  What does that mean?  And what exactly do we celebrate on Cinco de Mayo?