Robert's Rebellion, also known as the War of the Usurper, was one of the last great civil wars among the Great Houses of Westeros that took place approximately seventeen years before the War of the Five Kings begins, and lasted about one year; two, if one counts the Assault on Dragonstone as the final engagement of the conflict.
It began just after the execution of Rickard Stark, head of House Stark, and his son and heir Brandon by the Mad King, Aerys II. The end of the war saw the collapse of the Targaryen dynasty with the deaths of the Mad King and his son and heir, Prince Rhaegar, and the ascension of Robert Baratheon to the Iron Throne, thus beginning the Baratheon dynasty. Despite this, the Mad King's two other children were safely smuggled across the Narrow Sea to Essos: Viserys and Daenerys Targaryen.
Secretly, however, Prince Rhaegar had another son, this one with Lyanna Stark: Aegon Targaryen, who was raised by Lyanna's brother Eddard Stark as his own bastard son, Jon Snow, to protect the boy from those that sought the deaths of all the Targaryens after the war.
