In reference to Japanese history, Along with Minamoto, Taira was an honorary surname bestowed by the emperors of the Heian Period to the ex-member of the imperial family when they became subjects. This Taira clan is often referred to as Heishi (平氏).
Some grandsons of Emperor Kammu were first given the name Taira in 825 or later. Afterwards, descendants of Emperor Nimmyo, Emperor Montoku, and Emperor Koko were also given the surname. The specific hereditary lines from these emperors is referred to by the emperor's name followed by Heishi. i.e. Kammu Heishi
The Kammu Heishi line proved to be the most strong and dominant line during the late Heian period with Taira no Kiyomori eventually forming the first samurai dominated government in the history of Japan. The last of the head family of the Kammu Heishi line was eventually destroyed by the armies of Minamoto no Yoritomo at the Battle of Dannoura, the last battle of the Gempei War.
The Kammu Heishi had many branch families including Hojo, Chiba, Miura and Hatakeyama.
See also: Japanese name.