Cat communication is not limited to mows and purrs. Like all animals, they also communicate through body language. Posture is one of the most obvious ways that cats communicate their moods. When a cat exposes his stomach, he can be feeling and expressing aggression, playfulness, trust or love.
When a cat is ready to fight an opponent, he will sometimes lie down on his back. It might not seem logical for a cat to expose his stomach when he feels threatened, but this position actually allows him to make the best use of his natural defenses. If he is lying on his back, he can attack or defend himself with the claws on all four paws, as well as with his mouth. If this is his intention, it will usually be accompanied by growling, hissing and laid back ears.
Some cats will lie down and roll over when they are feeling playful. Keep in mind that his idea of playing likely mimics the attack or defensive posture, so he may be in the mood for roughhousing. In this case, his tail is likely to be swishing back and forth, but not excessively. Still, he might get carried away, so watch your hands.
Sometimes cats lying down on their backs near their humans as an expression of love. The stomach is the most vulnerable part of any animal, so exposing it is your cat's way of telling you that he trusts you completely. In this case, they asking for a caress or belly rub. Their other body language is also relaxed in this situation.
Some cats get on their backs to sleep. If your cat does this, it is a signal that he is completely relaxed around you and in his environment. He feels completely secure and trust you implicitly.