Like their descendants, wolves to, love a good belly rub!
Most canines love a good belly rub. Some canines love them so much they actually demand them. Dogs generally roll over on their backs for a nice belly rub from people they trust. It is, at it’s core, a submissive behavior.
Offering their belly is a sign that they trust you. It feels good and they don’t mind showing you this vulnerability for a nice old fashioned belly rub. The submissive behavior does not mean that the dog is enjoying the petting any less. Seems like a pretty fair trade off right?
A dog can express more with his tail in seconds than his owner can express with his tongue in hours. – Unknown Author
Rolling over to show you his belly leaves him physically vulnerable, and represents a strong degree of both trust in and submission to you. Rubbing his belly just plain feels good, much like other types of petting, but it also shows him that his trust and submission were well-placed, and that you won’t take advantage of his vulnerability.