I am guessing most Americans have absolutely no idea why they are celebrating Cinco de Mayo today. I am not being judgmental; there is no good reason why they should, given that it isn't something we have traditionally covered in school. Obviously, any excuse to eat guacamole is a good one, but in honor of the actual observance (hint: it has nothing to do with Corona), here is some historical background on a very interesting episode in Mexican history.
In the mid-1800s, France (yes, France... I'll get to the New World in a minute) was ruled by the monarch Napoleon III, who was the nephew of the original Napoleon. France wanted to expand its influence in Latin America, going so far as to actually coin the term "Latin America" in an effort to make it seem more natural that France (a Latin country) should be involved in the region. Meanwhile, Mexico itself was in its fourth decade of independence from Spain and embroiled in a civil war between liberal reformers and conservatives. In 1858, the liberals retook control of the capital, but meanwhile all this fighting had bankrupted the Mexican government. Liberal leader Benito Juárez suspended Mexico's foreign debt payments, and in retaliation France, Spain and Britain collectively occupied the vital port city of Veracruz. (Note this is the rare episode since the 1840s when the United States was not actually involved; refreshing. There was, however, a significant reason; more on that soon.)
Mexican conservatives were searching desperately for a way to overcome the liberals, and they turned to the idea of a monarch. This desire neatly dovetailed with Napoleon III's interest in imperial expansion, and he generously offered them a potential candidate: Maximilian, a member of the Hapsburg dynasty with the best of intentions for Mexico. Conservatives convinced him that yes, Mexicans really did want an Austrian emperor. France duly invaded Mexico in 1862.
The French faced significant opposition, and one of the most notable episodes is the event that gives us Cinco de Mayo. France was utterly convinced that it could walk all over the Mexican army with few obstacles. In a wonderfully misguided demonstration of the racial consciousness that characterized European thought in the 19th century, the French commander wrote to his minister of war on April 25: "We are so superior to the Mexicans in race, organization, morality, and devoted sentiments that I beg your excellency to inform the Emperor that as the head of 6,000 soldiers I am already master of Mexico." Meanwhile, the Mexicans had dug in at the city of Puebla, and on May 5, 1862, battle commenced -- resulting in a thorough defeat of the French army, which hightailed it back to Veracruz in shambles.
Unfortunately for the Mexicans, a glorious triumph in one battle did not end the war. In 1864, France succeeded in installing Maximilian on the Mexican throne (not that it exactly had one, given that it was originally established as a constitutional republic). Maximilian attempted to draw upon Mexican nationalist symbols, with very little success (duh). Meanwhile -- you knew we couldn't stay uninvolved for long -- the United States allied with Benito Juárez. France had clearly violated the Monroe Doctrine (hands off the Americas). We were a little busy in the early 1860s with our own Civil War, but when the war ended in 1865 our attention turned southward. Napoleon III decided to withdraw his own military forces from what had become a costly quagmire, and while Maximilian stayed in Mexico, he was quickly rounded up and executed. Loyal to his adopted country to the end, the poor guy is said to have uttered "Viva Mexico!" as he faced the firing squad.
References: John Charles Chasteen, Born in Blood and Fire: A Concise History of Latin America (Norton, 2006); Michael C. Meyer and William H. Beezley, ed., The Oxford History of Mexico (Oxford, 2000) [quote is taken from the latter, p. 381].