The Crow is a high ranking member of the Thieves Guild, and also a political faction associated with the Guild. Besides this, not much is known about him.
The Crow can be found in any carpenter's store. These stores serve no apparent purpose in the game. They can be found in any town which has a Bookstore, a Clothing Store and a Pawn Shop but neither a Gem Store nor a Library (use the corresponding tables of the Iliac Bay's regions to find such towns). Carpenter's Stores have the same sign as pawn shops, but they can be easily distinguished from them by their name.
When The Crow offers you a quest, it will be a standard Merchant/Innkeeper quest (rather than a Thieves Guild quest). Upon its completion, you will gain or lose reputation with The Crow, the Thieves Guild, and its associated factions.