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Though it was obvious, no?

Minister Hyden told us what Morai represents/embodies during the very same episode:
"She is a servant of the Daughter, or possibly the Daughter herself, when acting as a spirit guide."

ie. Morai = the Daughter = Ahsoka's spirit guide/friend. This also explains how Morai was able to just pop-into TWBW and knew which gateway Ezra needed to access in order to save Ahsoka.


As for why Ahsoka owes Morai her life, recall that during the Mortis Trilogy the Daughter transferred her essence into Ahsoka, thereby saving her life:
https://www.youtube.com/watch?v=kIf3qrJLcR0

The Daughter = Yue from The Last Airbender