A Heartstone is both an artificial node produced by the Tayledras and the node's physical anchor. Heartstones can be used by a mage of at least Master level, much like the pools of energy underneath Mage Schools. The knowledge of how to create a Heartstone was given to to the Tayledras by the Star-Eyed at the Sundering of the Clans.
The only known Heartstones not controlled by the Hawkbrothers are under the ruins of the palace in what was once Lineas and the palace in Haven. The first was left behind by the Tayledras because it was welding shut a fault line caused by the Mage Wars. The second was created with the knowledge that Savil and Vanyel gained while staying with the Tayledras, and anchors the second incarnation of the Herald Web. Mornelithe Falconsbane also attempted to create a Heartstone but failed, presumably due to the lack of divine instruction.
Heartstones seem to have a limited consciousness as evidenced by Vanyel "communicating" with the Linneas Heartstone.
Heartstones are created by the Tayledras to be a vessel in which to contain the magic cleansed out of the Pelagirs. Ley-Lines are re-routed by Adepts and Masters to drain entirely into the Heartstone, bringing the surrounding area back to normal. Once finished, the Clan will drain out the Heartstone entirely to establish a new Vale, and will Gate over to start the process in a new area.
The Heartstone present in k'Sheyna Vale was the only known case of a corrupted Heartstone. Mornelithe Falconsbane was able to manipulate Starblade k'Sheyna in order to weaken the Heartstone. Upon the conclusion of k'Sheyna's Cleansing, the Heartstone shattered, releasing the magical energy built up in the Heartstone violently.