1590s, "of or pertaining to Corinth," the ancient Greek city-state. The earlier adjective was Corynthoise (mid-15c.). From 1650s as an architectural order. As a noun, "inhabitant of Corinth," 1520s (Corinthies is attested from late 14c.).
In classical times among the other Greek states Corinth was noted for ornate architecture and notorious for its luxury and licentiousness (and for not scorning trade and profit); hence Corinthian, noun and adjective, in various slang or colloquial sense in English, especially "a swell, a man about town" (early to mid-19c. but especially 1820s).