A corestone is a magic jewel containing the soul of a dead being, that only Val and his ancestor Khoda have the power to create. It is described as the very essence of the being from which it is created.
Every monster that Val destroys, bosses included, leaves behind a corestone from which a special ability can be harnessed. However, it turns out to be much more important than it first seems, when Eoren performs a ritual to copy Val's power and sacrifices Hinna to get her corestone.
Khoda later explains that this power was first meant to return monsters to the flow of mana. Now, he uses corestones made from the soul of every alm making their pilgrimage to to sustain the Tree of Mana and keep Daelophos' curse at bay.