It's located under the roots of the World Tree, the tree on which the Hanged Demon is hanging. The demon asks Lara to retrieve it for him, and in return she would be rewarded. However, Lara never return the heart to its owner, because it's needed to gain access to the final part of the level.
The Demon's Heart is obtained by burning the roots of the World Tree with a lit torch. Then it's later placed to a certain niche to open a door.