Some TMNT stuff really isn't for little kids.
More details about the history of the Gosei Clan are not known, but it is a warrior clan with an ancient tradition in Japan's history. As of yet unknown means, the Gosei acquired the mystical ability to pass on the spiritual heritage of their clan to a designated successor, usually the next son. As a result, this meant that - when this transfer was completed - every new generation leader of the Gosei could access the entire skills and the overall knowledge of the martial arts of his ancestors, to become an even more invincible warrior.
This mystical transfer ability (and certainly others such experiments with the fabric of space) have also attracted the attention of the Keepers of Time. Perhaps these tests are also the inspiration for the Herald character of the clan: an infinity symbol (∞), which is flanked by two half-circles or crescents on the narrow sides.
The Turtles made acquaintances with the Gosei Clan for the first time in their childhood, as their master Splinter was contacted by Gosei Hatsumi on the astral plane. Hatsumi, the current bearer of the Gosei Clan heritage, was dying, and the legacy was threatened to be lost, because his son Kenji had turned his back on the traditions of his family and thus had created a gap in the sequence of the mystical transference. The last heir of the clan was Hattori, his only grandson, who already stood at the crossroads of his life.
With Splinter's consent Hatsumi took over his body to transmit his legacy to Hattori. After Kenji saved Hattori from a murder plot, Hatsumi managed to complete the transfer, and Hattori readily accepted his rightful heritage. Years later Hattori helped the Turtles on two other occasions: first, when the inter-dimensional sorcerer Savanti Romero tried to use the mystical abilities of the clan for his own sinister purposes; and at the time when Hattori, after he had become completely open with has legacy, was preparing to wipe out the criminal legacy of his father from the family history.