The Pledge of Immortality is a deal that can be made between a human and a mazoku to confer partial immortality.
When the human makes the deal, their soul is stored inside of a Pledge Stone. As long as the stone exists, they cease aging and recover instantly from any injuries suffered. They can only die under three conditions: if the Pledge Stone is destroyed, if the mazoku with whom they made the Pledge is destroyed, or if they are hit by a spell calling power from a being more powerful than the mazoku with whom they made the Pledge. (It is somewhat unclear whether only black magic spells can be used for this purpose.)
The mazoku who makes the Pledge with the human does not receive any immediate benefit from the deal. However, it does advance the long-term goal of increasing human suffering, as only an evil person would be willing to sell his soul to the mazoku, and such a person would not have good intentions for using their immortality. Presumably, if the human began proving difficult then the Pledge Stone could be used as a lever against him.