Minamoto (源) was an honorary surname bestowed by the Emperors of Japan of the Heian Period to their sons and grandsons after accepting them as royal subjects. As custom, in order to ease imperial succession and end rivalries for the throne, princes not eligible or far removed from the throne were given a surname and became subjects of the emperor.
The first emperor to start granting the name Minamoto was Emperor Saga. Afterwards, Emperor Seiwa, Emperor Murakami, Emperor Uda, and Emperor Daigo, among others, also gave their sons the name Minamoto. These specific hereditary lines coming from different emperors developed into specific clans and are often referred to as the Genji (源氏). These specific hereditary lines from these emperors is referred to by the emperor's name followed by Genji, e.g., Seiwa Genji.
The Seiwa Genji line proved to be the most strong and dominant Minamoto line during the late Heian period with Minamoto no Yoritomo eventually forming the Kamakura Shogunate and becoming shogun in 1192. Also, it is from the Seiwa Genji line that the later Ashikaga - founders of the Ashikaga shogunate, Nitta, and Takeda clans come.
The protagonist of the classical Japanese novel The Tale of Genji, Hikaru no Genji, was bestowed the name Minamoto for political reasons by his father, the emperor, and was delegated to civilian life and a career as an imperial officer.
See also: History of Japan