The Moonsingers or moonsingers are the priestesses of the Jogos Nhai, nomadic raiders of the Further East. However, their religion has spread over Essos as moonsingers were among the escaped slaves that founded Braavos.
Among the Jogos Nhai
Each band of Jogos Nhai is led by a jhat, a war chief, and a moonsinger, who takes the role of priestess, healer, and judge. Whereas jhats command in matters of war, raid, and battle, the moonsinger commands over any other aspect in the band's life. Males can be moonsingers, too. However, this requires boys to dress and live as women.
When a shipment of slaves of the Valyrian Freehold bound for Sothoryos revolted, seized the slave ships transporting them, and fled north, a group of enslaved women from the lands of the Jogos Nhai prophesied where they would find shelter: a lagoon behind a wall of pine-clad hills and sea stones, where frequent fogs would help hide the refugees from the eyes of dragonlords passing overhead. These women were moonsingers and, according to Braavosi history, their prophecy proved true. For that reason, the Temple of the Moonsingers is the largest in Braavos.
A Game of Thrones
A Feast for Crows
They were very important in the founding and early history of Braavos, but they still exist to this day. Beyond that, I don't expect they'll have much importance to the present story....