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 and were later worshiped by the First Men as well.