Origin and history of empire

mid-14c., "territory subject to an emperor's rule;" in general "realm, dominion;" late 14c. as "authority of an emperor, supreme power in governing; imperial power," in Middle English generally of the Roman Empire.

From Old French empire "rule, authority, kingdom, imperial rule" (11c.), from Latin imperium "a rule, a command; authority, control, power; supreme power, sole dominion; military authority; a dominion, realm," from imperare "to command," from assimilated form of in- "in" (from PIE root *en "in") + parare "to order, prepare" (from PIE root *pere- (1) "to produce, procure").

Not etymologically restricted to "territory ruled by an emperor," but used that way. The Empire, meaning "the British Empire," first recorded 1772 (it officially devolved into "The Commonwealth" in 1931); before that it meant the Holy Roman Empire (1670s).

[P]roperly an empire is an aggregate of conquered, colonized, or confederated states, each with its own government subordinate or tributary to that of the empire as a whole. [Century Dictionary] 

Empire as the name of a style (especially in reference to a style of dresses with high waistlines) is by 1860, in reference to the affected classicism prevailing in France during the reign of Napoleon I (1804-15). Second Empire is in reference to the rule of Napoleon III of France (1852-70). New York has been called the Empire State since 1834.