Today Madrid celebrates this day back in 1808 when the Spanish people rebelled against the French occupation. Spain was occupied by the French under Napolean Bonaparte, who began his conquest of Europe in 1807 by occupying Portugal.
When Bonaparte came to Spain, King Charles IV was forced to abdicate his throne to his son Fernando VII, and both of them were sent to Bayonne in France. The rebellion in Madrid was triggered when the French tried to move King Charle's children to France too.
The uprising began infront of the Royal Palace, and spread to the barrios of Sol and Malasaña -- in Malasaña there is even a plaza called "Dos de Mayo" (2nd of May) that marks a key area of bloodshed. Thus began the Spanish war for independence.
The insurgency was supressed brutally and quickly, but marked the beginning of many larger scale rebellions to come. Most people were killed and most of those who survived the battle were executed the next day.
The leaders of this rebellion were Luis Daoíz y Torre, Jacinto Ruiz y Mendoza and Manuela Malasaña -- statues of these local heroes can be seen in various points in barrio Malasaña.
Today is a national holiday and to celebrate the bicentennial of this important day in Spanish history in Madrid, there are multiple events around the city.
Artist Goya's paintings of this uprising are paraded around town, there will be a theatrical show enacting the occurings of May 2 1808 in Plaza de Cibeles, bands will be playing in barrio Malasaña, and fireworks/festivities will also be seen infront of the Royal Palace. So these are the spots worth going to if you want to be a part of the celebrations.
However, last year there were riots in Malasaña, not uncommon when so many people get together in an event that has political significance. So, although security is on high alert mode, be careful and attentive to what's happening wherever you go!