As humans, when we express certain non-verbal feelings towards another person, they will understand and if they feel the same way, they will express that non-verbal emotion right back. Cats are highly sensitive when it comes on to emotions and humans. They may not have been blesses with the facial expressions that may go along with those emotions but they are there. Cats can express, trust, love and emotion towards you by doing various bodily movements, making sounds and being close as possible to you. They do understand when you are ill, angry or as expressed love to them verbally. They can sense the truth of tone in your voice and knows genuine emotions and feelings than if you or someone was actually faking it.
Cats Do Understand Gestures
This is true. Depending on the type of cat and character, some cats do understand hand gestures and respond to them accordingly. My cat named Tiger was trained to come to me whenever i lowered my hand and rub my thumb over my other fingers repeatedly. She would just stop whatever she is doing and stroll right over.
Responding To Sound
Cats can tell whether the have the green to go or red means stop by the tone in which the command is executed. sound of tone plays a lot to not only do with cats lives, But us as humans too. Telling some one to stop while giggling may mean something different that telling someone to STOP! with a strong exclamation sign. Cats recognize tones and understand that firmer, assertive tones may mean that whatever they are ding is not acceptable by their owner and should desist from doing so. But as with any animal, everything takes time.
Understanding The Language
Many people will like to beleive that cats understand the spoken language but they have no time to understand the complexity and many times stupid rules of man languages. The cat simple associates a spoken tone with many times a gesture that is repetitive and then that tone becomes locked to the action without even the gesture.
In conclusion, cats do understand humans to an extent even more than we understand cats. There is always something mystifying about the feline which makes them a good but very interesting pet.