1590s, "a sending abroad," originally of Jesuits, from Latin missionem (nominative missio) "act of sending, a despatching; a release, a setting at liberty; discharge from service, dismissal," noun of action from past participle stem of mittere "to send," oldest form probably *smittere, of unknown origin.
Diplomatic sense of "body of persons sent to a foreign land on commercial or political business" is from 1620s. In American English, sometimes "an embassy" (1805). Meaning "dispatch of an aircraft on a military operation" (1929, American English) later extended to spacecraft flights (1962), hence, mission control (1964). As a style of furniture, said to be imitative of furniture in the buildings of original Spanish missions to North America, it is attested from 1900.