The Blackfyre Rebellion was an uprising led by Daemon Blackfyre, a legitimized bastard of King Aegon IV Targaryen and his cousin and lover Daena Targaryen, against his half-brother, King Daeron II Targaryen. The rebellion failed, and Daemon himself was killed in the Battle of Redgrass Field.
In the books
House Blackfyre fled east to the Free Cities, and continued to harass the Targaryen kings for decades. There were as many as Five Blackfyre Rebellions over the course of sixty years, but of varying size. The first was also the largest, and the one which very nearly succeeded due to the popularity of Daemon. The "Second Blackfyre Rebellion" was little more than a plot which was rooted out before it could achieve fruition. The fifth and final Blackfyre Rebellion was known as the War of the Ninepenny Kings.