mid-15c., "lordship, sovereign or supreme authority," from Old French dominion "dominion, rule, power" and directly from Medieval Latin dominionem (nominative dominio), corresponding to Latin dominium "property, ownership," from dominus "lord, master," from domus "house" (from PIE root *dem- "house, household").
In law, "power of control, right of uncontrolled possession, use, and disposal" (1650s). From 1510s as "territory or people subject to a specific government or control."
British sovereign colonies often were called dominions, hence the Dominion of Canada, the formal title after the 1867 union, Dominion Day, the Canadian national holiday in celebration of the union, and Old Dominion, the popular name for the U.S. state of Virginia, first recorded 1778.
c. 1600, "territory over which dominion is exerted," from French domaine "domain, estate," from Medieval Latin domanium "domain, estate," from Latin dominium "property, dominion," from dominus "lord, master, owner," from domus "house" (from PIE root *dem- "house, household"). A later borrowing from French of the word which became demesne.
Sense of "dominion, province of action" is from 1727. Meaning "range or limits of any department of knowledge or sphere of action" is from 1764. Internet domain name is attested by 1985. Via the notion of "ownership of land" comes legal eminent domain "ultimate or supreme lordship over all property in the state" is attested from 1738.