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.