The bow was said to have been carried into battle by Auri-El himself against the forces of Lorkhan during the Ehlnofey wars of the Dawn Era. When Trinimac defeated Lorkhan and tore out his heart, Auri-El fastened it to an arrow shot it long into the sea, where Red Mountain eventually formed. 
Auriel's Bow has changed hands several times over the years. The artifact was once found by the Eternal Champion in his quest to overthrow Jagar Tharn. It was later rewarded to the The Hero of Daggerfall by an unknown person after he was helped. Many years later the Nerevarine acquired the bow for Lady Therana, a mad Telvanni councilor. It then wound up in the Inner Sanctum of the Forgotten Vale, in the custody of two Snow Elves.
Auriel's Bow appears in the following games: