Short answers, pulled from the story.
The Third of May 1808 was completed in 1814, six years after the events it depicts. Goya approached the provisional Spanish government in February 1814 with the proposal to paint commemorative works after the final expulsion of the French.
The painting depicts the French reprisals that followed the Dos de Mayo Uprising in Madrid. Before dawn on the 4th of May 1808, French forces rounded up and shot hundreds of Spaniards at several locations around the city, following a popular rebellion against the French occupation the previous day.
The painting is in the Museo del Prado in Madrid. It has left Madrid only once, when it was transported by truck to Valencia for safekeeping during the Spanish Civil War.
Art historian Kenneth Clark described it as "the first great picture which can be called revolutionary in every sense of the word, in style, in subject, and in intention." Unlike earlier depictions of violence, Goya replaced individual heroism with anonymity and futility, subverted the traditional spiritual role of light, and offered no cathartic resolution, making it one of the first paintings of the modern era.
The painting inspired Gerald Holtom's peace sign and a series of paintings by Edouard Manet. Pablo Picasso also cited it as a reference for Massacre in Korea and Guernica.
The provisional government of Spain commissioned the painting at Goya's own suggestion, shortly after the ousting of the French and the restoration of Ferdinand VII. Goya proposed to "perpetuate by means of his brush the most notable and heroic actions" of the Spanish insurrection.