It's because as the coffee dries, the liquid gets pulled to the rim, leaving all the coffee gunk behind in a ring. Turns out, this same trick helps make better inks and paints too!
I once noticed on a neighbor's garbage can, which had their house number spray painted on it, that the paint had mostly flaked off except around the edge of the numbers which was adhered better. The paint would have been thinner from the spray application.
