What does Cinco de Mayo represent for the Mexican population?

Cinco de Mayo (May 5) is a celebration of the Battle of Puebla (May 5, 1862) when Mexican forces at first defeated the French forces that had invaded under an agreement between Britain, Spain, and France. French reinforcements ultimately won the war and occupied Mexico City in 1863, But Napoleon III recalled the troops in 1866 (partly due to pressure from the US), leading to the end of the Second Mexican Empire and the execution of Maximilian I.