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The belly-up position, in which your cat will roll to one side and show its tummy, is indeed very meaningful among cats, with significance for cat and human relationships too. Like many mammals -- including us -- when the back is against the floor and the stomach and chest areas are exposed, the individual is more vulnerable than it would be if it were standing. On the other hand, this position also allows your cat to put all claws and teeth to use.
Pam Johnson-Bennett, author of Cat vs. Cat: Keeping Peace When You Have More Than One Cat, explains how this belly-up position can therefore signify that your cat is in a defensive -- and not offensive -- mode. You might, for example, see two cats hissing at each other, preparing to fight, with one suddenly dropping down into this tummy-revealing position. Woe to the cat that doesn’t back down, because it will otherwise receive a face full of claws and teeth.
On the other hand, Johnson-Bennett explains that cats will also go into belly-up mode when they are feeling incredibly relaxed and playful. In this case, the move communicates that your pet is in the mood for a bit of harmless roughhousing, with no intention of taking the offensive position.
It clearly pays to know which of these two meanings is being communicated. An easy clue is to look at your cat’s ears. If they are held back against your cat’s head, beware. If they are up and forward, chances are your cat wants to just play and have some fun.