Cats are natural predators, despite being domesticated, so often what they think about is how to expend their energy in ways that get them a mouthful of food. This is why an apparently relaxing cat takes such an immediate interest in small movements from strings, feathers or lasers.
In the wild, cats think about how to hunt, kill and eat, so even on a domestic level those are still their thoughts. According to British anthrozoologist John Bradshaw, cats were never bred to fill a specific domestic role like dogs historically were, thus they retained much more of their natural or wild behaviors. They interact with feral cats often, accounting for as many as 85 percent of kittens who are born at least partially feral. This also helps keep their brains functioning in much the same way as they functioned prior to domestication.
With a ready food supply, however, a domestic cat has more free time, so her thoughts of hunting extend into actions that look more like playing but which still expend the same movements and energy as hunting. Crouching, pouncing, batting and clawing are all examples of this behavior. So is simply alert watchfulness.
In terms of non-hunting thoughts, cats seem to think of people as their parents. They socialize with humans in the same way they socialize with other cats, specifically mother cats. While a dog has a different set of behaviors he displays towards humans, a cat does not change her behaviors towards humans. When she rubs against a person or kneads him, she is expressing the same social behavior as she would with her natural parent.