A domain is described as a fundamental and inalienable law of the world. It is the territory where a Devil Beast King was born and the source of that King’s power: the further a King goes from it, the weaker he becomes. Each domain has its own “magical wavelength”; entering the wrong one normally causes a pushback.
Domain power is not limited to the Kings. The Books of Toa give off the power of a domain, which is how the book at Solsein gives its holder absolute control of the school grounds. Clevatess learned to convert the leaking power of the Furnace book into his own. The hero Wright’s skill “Librarian” infused books with domain power, and the Chamber above the clouds is a special area where any domain-holder in humanoid form can use their power. Luna shows signs of possessing domain power himself.