From Harvard Health Publication:

“We need careful planning of our movements, decision making, reaction time, and attention,” says Brad Manor, PhD, an instructor in medicine at Harvard Medical School and director of the Mobility and Falls Program at the Harvard-affiliated Hebrew SeniorLife in Boston. “Staying mentally active is very important to avoiding falls.”
We depend on several body systems to keep us upright. The inner ear, which senses head motions, has an important role. So does the body’s somatosensory system, which relays the feeling of the ground beneath your feet. And, of course, vision tips you off to obstacles around you. The brain takes in all this information, plans out movement, and carries it out. “Balance is a complex system,” Manor says. “Especially as we get older, cognition becomes a big part of it.”
Manor and his fellow researchers are conducting studies to evaluate the balance benefits of tai chi, a form of exercise that involves moving gently through a series of poses. Tai chi improves balance because it works with both the mind and body.
You could also perform daily “standing balance” exercises. These include repeated moves that involve standing on one leg while gently lifting the other. A personal trainer can also help you learn a balance-improving routine.  
Maintaining mental fitness, remaining physically active, and practicing tai chi, qigong, yoga, or some other mind-body exercise can help you keep your balance and avoid stumbling. But if you do lose your balance, recovering requires muscle power. Power is the ability to exert force quickly — the kind of conditioning an experienced ballroom dancer uses to “push off” during quick steps and returns. Rapid, forceful exercises like hopping and side stepping help to build power. For beginners, classes or trainers are valuable to learn how to exercise for power safely.