House Targaryen is a Great House of Westeros and was the ruling royal House of the Seven Kingdoms for three centuries, before it was deposed during Robert's Rebellionand 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".
(source Game Of Thrones wiki)
The Windsors (British royal family) of Earth are distant relatives of both the Targaryens and Baratheons