Hircine's Ring is a Daedric artifact, a ring which was created by the Daedric Prince Hircine. In The Elder Scrolls III: Bloodmoon, it has the power to turn the wearer into a Werewolf for a certain time.
The Nerevarine had to compete against Hircine in a ritualistic hunt. As a result of the betrayal from the Skaal Chieftain Tharsten Heart-Fang during the hunt, the Nerevarine had to kill him. Once that is done, Hircine's Ring will appear on the finger of the Nerevarine.