I found answers on many web sites and they differed too much so I decided to ask the community.
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I call him the devil because he makes me wanna sin... Urban Dictionary
A good-looking cheeky fellow. Yahoo! answers
Symptoms of being a handsome devil include being good-looking, rich and a jerk. Often a playboy.
TV TropesThe very Devil, himself, is supposed to look amazingly-charming, and can attract almost any woman. Therefore, a guy who's " devilishly handsome / good-looking " is a man who looks so attractive, especially to the opposite sex, that the women swoon over him, in huge numbers. Yahoo! answers
It's a very common expression, used as a compliment of sorts. It is used to compliment someone, a man, but at the same time, usually to give a little jab, like saying "You're a handsome man, and you're very much aware of it. Word Reference