Short answers, pulled from the story.
The Dos de Mayo Uprising was a rebellion by the civilian population of Madrid against French military occupation, which took place on the 2nd and the 3rd of May 1808. It was largely spontaneous, lacking formal planning or elite leadership, and was violently suppressed by French Imperial forces with hundreds of public executions. The uprising triggered the Peninsular War and ended the Franco-Spanish alliance in the Napoleonic Wars.
The immediate cause was Marshal Murat's attempt to move Francisco de Paula, the youngest son of deposed King Charles IV, and other royal family members from Madrid to Bayonne, France. A crowd gathered at the Royal Palace to prevent this removal, and when Murat responded with grenadiers and artillery that opened fire on the crowd, the rebellion spread across the city.
Luis Daoíz y Torres and Pedro Velarde y Santiyán were the two artillery officers who disobeyed orders and joined the Dos de Mayo Uprising at the Monteleón barracks in Madrid. Velarde was a 28-year-old artillery captain who had been secretly planning military action elsewhere but was drawn to the sound of gunfire on the 2nd of May 1808. Both died when French forces stormed the barracks, and both are still commemorated as heroes of the rebellion.
Marshal Murat imposed martial law, moved the majority of his troops into Madrid, and established a military commission on the evening of the 2nd of May 1808 chaired by General Grouchy. The commission issued death sentences to all prisoners found carrying weapons of any kind. Hundreds were executed on the 3rd of May; craftsmen carrying everyday tools such as scissors or kitchen knives were shot alongside those who had actively fought.
The French repression of the uprising, including the mass executions on the 3rd of May 1808, spread outrage beyond Madrid. In the town of Móstoles, Juan Pérez Villamil encouraged mayors Andrés Torrejón and Simón Hernández to sign the "Bando de los alcaldes de Móstoles," a declaration calling all Spaniards to rise against the French. This national call to arms, combined with Napoleon's installation of his brother Joseph as king, turned a local revolt into a country-wide guerrilla war.
The 2nd of May is a public holiday in the Community of Madrid. The site of the Monteleón artillery barracks is now the Plaza del Dos de Mayo, and the surrounding district is called Malasaña after Manuela Malasaña, a teenager executed by French troops after the revolt. Francisco de Goya's paintings The Charge of the Mamelukes and The Third of May 1808 are the most famous artistic records of the events.