"The battle at Puebla in 1862 happened at a violent and chaotic time in Mexico's history. Mexico had finally gained independence from Spain in 1821 after a difficult and bloody struggle, and a number of internal political takeovers and wars, including the Mexican-American War (1846-1848) and the Mexican Civil War of 1858, had ruined the national economy." [source: mexonline.com]
So why do we celebrate Cinco de Mayo in the United States? Well, some sources say that the battle at Puebla slowed the French army down and provided U.S. and Northern Mexico territories an opportunity to set up a much better equipped (and larger) Mexican army. The United States was in the middle of a civil war between its own states while all this was happening in Mexico, so both Countries were pretty much on their own. Mexico's first victory (on May 5th) gave the entire Country a huge boost in confidence. The news of the victory gave all of Mexico the courage to continue the fight when the French army returned.