A Pledge Stone is the physical embodiment of a Pledge of Immortality made between a human and a mazoku. When the deal is made, the human's soul is sealed inside the stone. From that point on, the human does not age and recovers immediately from any injury. Any physical object can be used as the Pledge Stone, allowing it to be easily hidden.
The only human currently known to have made a Pledge of Immortality is Halcyform the White, who made the deal with Seigram the Formless. In the anime, this was to save his life after being severely wounded in an accident; in the novels, to further his goal of attaining true immortality.
In both versions, Halcyform's Pledge Stone was a mask worn by Seigram. Lina Inverse figured this out and broke the mask. Halcyform survived the immediate destruction of the stone, due to having earlier consumed the essence of Gio Gaia, but lost his immortality and died soon after.