I think that when you say something like "show me your belly" it has a particular sound. If you rub his belly after he does it and he likes it, he probably remembers the way it sounds coming out of your mouth, so when he hears that sound again he knows what to do. It's the same concept with why they seem to know their names and answer when we call them. They recognize that sound as what noise you make when you call them. I do kinda wish we could talk to each other... I would love to hear what my boys have to say from time to time!
OK, I've got a great story for this. Back when I only had Levi & Jordan they would wrestle really hard. Inevitably one of their collars would pop off. One day I came home to find Levi without his collar. I couldn't find it so when Jordan came over by me I looked at him & said where's your brother's collar? I'm not kidding not 10 seconds later he carried it over in his teeth and dropped it at my feet. Talk about freaking me out. I had never asked him this question before. of coarse I've tried it since then and it's never worked again, but that one time was enough to prove to me just how smart he is.
My kittens are slowly learning. They know what 'No' means and "Be nice" for when we're playing with them and they get a bit too rambunctious with their claws.
I have been told by horsemen that when you speak, in whatever language, your thoughts are clarified & that's what cats are really responding too. Supposedly, horses and cats communicate that way and some race horses have a companion cat that travels with them because cats are small to truck along with a horse.
My mom can talk to my cats in Spanish & they understand
The first time she told JC, "You stay out of my kitchen!" he stopped at the kitchen entrance, looked at her, swished his tail, looked at the kitchen, then made a hard left and sauntered down the hall