House Targaryen is a Great House of Westeros and was the royal house of the Seven Kingdoms for three centuries, before it was deposed during Robert's Rebellion and House Baratheon replaced it as the new royal House. The few surviving Targaryens fled into exile. Currently based on Dragonstone, House Targaryen seeks to retake the Seven Kingdoms from House Lannister.
House Targaryen's sigil is a three-headed red dragon on a black background, and their words are "Fire and Blood".
The House currently fields an army of 100,000 Dothraki, 8,000 Unsullied and 2 dragons. These combined with the various smaller houses who have sworn themselves to Daenerys’s cause make the House the most powerful in Westeros.
(source Game Of Thrones wiki)
The Windsors (British royal family) of Earth are distant relatives of both the Targaryens and Baratheons