Found in a chest in the area of The Duke's Archives just before you exit to the courtyard before the Crystal Cave.
Unlocks the large cell at the bottom of the tower where you were imprisoned. If you have been assisting Big Hat Logan, the Archive Tower Giant Cell Key is required to free him. Otherwise, this key will grant you a generic Fire Keeper Soul.
The Archive Tower Giant Cell
is located at the very bottom of the area after your first encounter with Seath the Scaleless. The key however is near the end of The Duke's Archives area.
credit: From Software