Someones who's really vain and makes an unecessary effort with their appearance e.g. a well oiled, beautifully bronzed sunbather at a tourist resort, or a cool kid with too much gel in their hair. The phrase was first used in german (lackierter Affe), and is a lovely description of that loathsome type of person.
Arnie: "Check out my beautifully oiled biceps"
Sally: "Wow! You're a real varnished monkey!"