An empire is a State with politico-military dominion of populations who are culturally and ethnically distinct from the imperial (ruling) ethnic group and its culture  — unlike a federation, an extensive State voluntarily composed of autonomous states and peoples. As a State, an empire might be either territorial or a hegemony, wherein the empire’s sphere of influence dominates the lesser state(s) via divide and conquer tactics, i.e. “the enemy of my enemy is my friend”, (cf. superpower, hyperpower).
What physically and politically constitutes an empire is variously defined; it might be a State effecting imperial policies, or a political structure, or a State whose ruler assumes the title of “Emperor”, thus re-denominating the State (country) as an “Empire”, despite having no additional territory or hegemony, e.g. the Central African Empire or the Korean Empire (proclaimed in 1897 when Korea, far from gaining new territory, was on the verge of being annexed by Japan). The terrestrial empire’s maritime analogue is the thalassocracy, an empire comprehending islands and coasts to its terrestrial homeland, e.g. the Athenian-dominated Delian League.