Cinco de Mayo (May 5) is slightly celebrated in the US, less so in Mexico, with the exception of Puebla, where this particular battle was fought between the native Mexicans and the invading French troops, sent to Mexico by Emperor Napoleon III, looking for colonies in North America. On Cinco de Mayo, 1862, about 2,000 Mexican soldiers, seriously outgunned and poorly equipped, defeated 6,000 French soldiers.
The Battle of Puebla is just one battle in Mexico's hard fought was for independence from France, and the victory was short lived. The French soon invaded with 30,000 men and installed Maximilian as Emperor of Mexico.
So why is it important, beyond being a feather in Mexico's hat? The United States was deeply involved in the Civil War, War Between the States, War of Northern Aggression, whatever you want to call it. Those French soldiers were not going to stop. They intended to invade the US. All the troops who might have been available to fight them at the border had gone north to fight the Union.
Napoleon III hated the US, possibly due to the unfairness of the Louisiana Purchase. Those troops were going to occupy mush of the west while the US could not possibly fight them. Or, they were going to fight for the Confederacy. Either way, US history would have been altered. Not, I think, greatly, but possibly.
Regardless, it kept the French away from the border. Which allowed the US to supply the Mexican Resistance with modern rifles, artillery, and Gatling guns.
Noting this, it is not really celebrated enough in the US. It is a fine excuse to party. So down a few of those quality Mexican beers, eat some Mexican food. Stop telling Mexico to build a wall.