It pretty open to interpretation, but it's typically used to mean "appearing to be of good breeding." How the individual interprets that is going to vary. Different people consider different features to be "noble."
Although it doesn't take too much time looking at photos of past aristocracy to figure out that, what with small gene pools and the like, fine features were def. not necessarily present.
To wit: a royal portrait of Henry V, from Wikipedia...and, go figure, these portraits were typically done in the most flattering way possible...and this is still the most that could be done.
https://upload.wikimedia.org/wikiped.../7f/Henry5.JPG
So much for "aristocratic" good looks.
Aristocracy means, and meant, money (and the requisite social standing). Looks don't really have anything to do with being "aristocratic," and good ones are as happenstance as they are with the rest of the population (if not less guaranteed, due to the degree of inbreeding historically amongst the aristocracy.
But, all that reality aside, yeah, "aristocratic" in the context of good looks is just a way of saying "appears elegant or refined." Whatever that means to you.