Azura’s Star is an artifact of the Daedric Prince Azura, and is one possible reward for the quest “The Black Star.”
During the second half of the quest, the choice to give the star to Aranea Ienith will lead to the Dragonborn being offered to keep it.
Like regular Soul Gems,it has the ability to trap white souls, or those of creatures. These souls can be used for enchanting or recharging. Azura’s Star will not disappear upon use, unlike other soul gems, allowing you to trap another soul after use.
Souls will fill the item before Soul Gems, meaning that Azura’s Star could possibly end up trapping the soul of a lesser creature instead of the desired target. Followers wielding weapons with Soul Trap can use the star to capture souls.