To find a Black Soul gem, go to the mountains west of Cheydinhal to a place called The Dark Fissure, a Necromancer's cave/altar. Easier way to find this place is by going through the Mage's Guild questline. When you go reach there, activate the altar and one should be inside. They are other Necromancer altars spread around Cryodill.
And the purpose so far is to sacrifice it to one of the Daedric Shrines. I don't know if it's any more powerful than a Grand Soul gem, but they sell for a lot.
__________________ We've broken down
We've broken out
But you will never follow
You've watched us drown
You've pushed us out
But we will never follow Will Photograph for Food...... | 
black soul gems 
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