Short answers, pulled from the story.
The people of Madrid rebelled against French troops after news that the Spanish royal family planned to leave for France. Marshal Joachim Murat issued a proclamation ordering that all those arrested with arms in hand would be shot.
Francisco Goya began work on the painting in February 1814 after approaching the provisional government of Spain. He completed it two months before creating its companion piece The Second of May 1808.
Hundreds of Spaniards were rounded up and executed at various locations around Madrid including Príncipe Pío Hill before dawn on the 3rd of May 1808. The rebellion initially began in Puerta del Sol square where cavalry charges occurred.
Gerald Holtom designed the peace sign based on imagery from this painting. The composition influenced later works such as Pablo Picasso's Guernica created in 1937 and Massacre in Korea painted in 1951.
King Ferdinand VII kept the work in storage because popular revolts were not regarded as suitable subject matter by the restored Bourbons. His preference for neoclassical art also contributed to the lack of commentary and exhibition until the painting appeared in the Prado catalog in 1872.