If you train in oriental martial arts, tai chi, or yoga, you will eventually run into a concept called 'chi' (also spelled qi and ki). This is a mystical 'life energy' in many Asian belief systems. Most of the people who developed martial arts believed in it, and this belief is embedded in traditional teachings. Some people still believe in it wholeheartedly, and swear that it is real and that it gives martial artists their power. But, at least in Cuong Nhu, most people have a modern scientific view of the world. We don't actually believe in magic energy flowing around the body, but we will still use the word 'chi' as a shorthand for a variety of things like mental focus, breathing, stamina, balance, pressure points, and soft flowing techniques.
So when someone says 'focus your chi' they mean 'control your breathing, get your mind in gear, and make sure you are well-balanced, relaxed, and alert.' When they say 'mess with his chi' they mean 'use techniques that knock him off balance, attack his pressure points, break his focus and concentration, and/or do something to take the fight out of him without using use brute force.' It is just a convenient way of talking about a variety of subtle things that we learn how to do, the little tricks of mental and muscular control that define martial arts just as much as learning how to hit things harder.
Chi can also mean knowing how to use the placebo effect to heal yourself. There are a lot of subtle ways that your mind can affect your body. Every medical study ever done has to account for the fact that people who think they are being healed will actually heal, without any real drug being administered. If you believe that something will heal you, then that thing can heal conditions that respond well to placebos, like minor pain and drowsiness. When you combine this with the fact that yoga, tai chi, and martial arts can be eally really good at strengthening your muscles, bones, joints, ligaments, tendons, and cardiovascular system, it is easy to see why people might attribute magical powers to these activities.