"the sea between southern Europe and northern Africa," 1590s, earlier Mediterranie (c. 1400), from Late Latin Mediterraneum mare "Mediterranean Sea" (7c.), from Latin mediterraneus "midland, surrounded by land, in the midst of an expanse of land" (but in reference to the body of water between Europe and African the sense probably was "the sea in the middle of the earth"); from medius "middle" (from PIE root *medhyo- "middle") + terra "land, earth" (from PIE root *ters- "to dry").
The Old English name was Wendel-sæ, so called for the Vandals, Germanic tribe that settled on the southwest coast of it after the fall of Rome. The noun meaning "a person of Mediterranean race" is by 1888.