Balance is a derivative of strength.

If you want to improve your balance, then getting your base strength up is the fastest way.

As we age, we don't lose something called "balance". We lose our strength as our muscles start to deteriorate.  The best thing an elderly person can do it keep from falling is to increase their base strength which will increase their balance.

For younger people, I often see videos of them trying to improve their balance by holding on to dumbbells and standing on one leg on an unstable surface.  Not sure if this is effective as they think it is.

I think most people would be better served to focus on getting their base strength up in natural human movement patterns like the squat, deadlift, overhead press and the bench press and would find this to be the single best lever you can pull for balance.