Yes, I think they probably understand a lot more than they care to let on, and more than we are clever enough to pick up on. It is true that they can train us - but it is also true that we can train them, or rather, we can work with them collaboratively so that they do certain things when we ask - like "sit" "speak" "lie down" and so forth. It's all in the approach - and varies from cat to cat, as far as the cat's interest in playing along. I had one cat who liked to be sung to. My cat Indigo gets off me if I sing - I think her ears are sensitive, and she doesn't like the sound radiating up through my chest into hers as she is lying on me. Or maybe she is just irritated because I am not paying sole attention to her. Each cat is unique, isn't it?