Who is Leah, exactly?

Leah is referred to as the adopted daughter and the niece of Deckard Cain, but she is actually the daughter of Adria the witch and Prince Aiden which makes her the granddaughter of King Leoric (AKA the Skeleton King ). Recall that Diablo attempted to possess Leoric, failed because he was too weak, then possessed his young son Prince Albrecht - Leah's uncle. Suffice it to say, the family has some bad luck.

Edit:

I recently found out that if you'd like to know more about how Cain and Leah met, there is a book from Blizzard called Diablo III: The Order which details there meeting and a whole lot of backstory leading up to Diablo III. Sadly it seems pretty light on details of what became of the heroes from Diablo II - at least based on the reviews I've read.

She is the daughter of Aiden and Adria. She is also the granddaughter of King Leoric.

Leah then is trained by Adria to harness the power of the black soulstone in which Azmodan and Belial will get trapped. Then Adria will reveal that Leah is her and Diablo's daughter, and will fuse the black soulstone with Leah to make her become Diablo as the prime evel, holding together all the souls of all the evils. When Diablo is slain, no trace of Leah's fate is told.

source