A heart tree is the center of a Godswood. It is a Weirwood tree that has a face carved into the wood of the trunk. Heart trees are sacred in the religion of the Old Gods of the Forest, and the closest thing to a "shrine" that the religion possesses.
Weirwoods have red sap, which leaks out of the deep cuts in the trunk made for the eyes of the faces - giving the appearance that they are weeping tears of blood. The faces are thought to have been carved by the Children of the Forest.