Before he was a Crusader, Bragi was a holy worker who received the teachings of Saint Maera. He was originally to be sacrificed to the Dark God, but a bishop who followed Maera saved him and raised him on an island located north of Agustria.
After Bragi became a Crusader and the Empire was destroyed, he came back to the same island he grew up on and saw that the Maera priests were all slain by the Empire. He then decided to build the Bragi Tower there to mourn their deaths as well as tell the world that there were people in the Imperial inner circle and the Loptr Church who saved the people, at the cost of their own lives. Over time, the true purpose of the tower would be forgotten, and by the time of Genealogy of the Holy War, rumor stated that the tower was built as a place where his powers could be sealed. After this, Bragi created the Church of Bragi, and his religion spread and became very popular.
In Fire Emblem: Thracia 776, the Bragi Sword is revealed. It isn't stated what Bragi had to do with this sword, but considering that the Loptous Sword was "cursed" by the Loptr Church, the Bragi Sword was probably "blessed" by Bragi.
Bragi is the god of poetry in Norse mythology.