When a dog rolls on its back, it is often a sign of submission. This is a way for the dog to show that it is not a threat and that it is not going to fight.
When a dog rolls on its back and exposes its belly, it is saying, "I trust you and I want you to rub my belly."
Sometimes, dogs roll on their backs to relieve an itch. This is especially common if the dog has an itch on its back that it cannot reach.
Some dogs roll on their backs to mark their territory. This is done by releasing pheromones from their scent glands.
Rolling on the back can also be a sign of trust and affection. This is especially common in dogs that are very close to their owners.
Sometimes, dogs roll on their backs as a way to play. This is often done when the dog is playing with another dog or with a person.