Azura's Star is the reward for the quest received at the Shrine of Azura. It functions as a unique, reusable Soul Gem which is not consumed when used for enchanting or for recharging enchanted items. It can hold any creature's soul, up to and including those of Grand level. However, a Black Soul Gem is required to capture sentient souls.
Azura's Star is one of the main items, like the Skeleton Key, that completely eliminates an otherwise important problem facing the player throughout the game. In this case, once one acquires Azura's Star and possesses a moderate level of Mysticism and Conjuration control, the player will never need to pay for recharging items again. Also, if paired with the Umbra Sword from the Clavicus Vile's Shrine quest, one can keep numerous enchanted weapons at any time. Azura's Star can also be used at an enchanting altar without it disappearing. If dropped and lost, the character who gave the player the quest will provide a new one after a chiding to look after it better and not lose it again.
Martin Septim may have sent the Hero on a search for Azura's Star, to help in his ritual for opening a gate into Mankar Camoran's Paradise in the quest Blood of the Daedra. Although the item was specifically asked for, any Daedric artifact would have sufficed.