Martial arts is all about manipulating balance- keeping yours and disrupting your attackers.
How can you hope to defend yourself if your own balance is out of whack and you are falling over or tripping all the time? You need to be able to experience and control your balance throughout a wide range of motions on your way to understanding motion.
Exercises that work and promote learning balance is the starting point.
Everyday balance is different than the balance used in martial arts. Being able to shift your balance, maintain it as you interact with your training partner, and keep it while applying a technique is vastly different then getting up off the couch and not falling over. Start off by balancing on one leg and then slowly move on to leaning your upper body forward and backwards while keeping your back straight. Bend your base leg to help compensate- starting out, feel free to use your arms to help balance yourself.
From that try the same exercise with your eyes closed. Without your eyes to compensate for the equilibrium you are going to have to rely on the “feeling” of your leg/body in contact with the earth to adjust your balance.
If you go off balance do your best to recover! Feel comfortable with that? Move on to adding some height, perhaps balancing on a beam or bench. We all have a tendency to rely on our “eyes” for balance and as a martial artist you want to reply on your body feeling for balance as your eyes can deceive you depending on height/light.
Work on some of these balancing “games” along with stretching.