This stat makes it possible to 'Tank' hits so-to-speak. It allows you to take a hit and still continue with your actions without interruption, the higher this number the more hits you can take, depending on the enemy aswell.
An armor's Balance can be increased with upgrading, though the effect is not shown on the armor piece itself.
To calculate the maximum Balance a piece of armor will have, take the base Balance and add 94.6% onto it. Round the tenth decimal according to the hundredth; that is the Balance at the maximum upgrade (VII).
Example: Palatine Chainmail has 10 Balance at base (unupgraded). 10 + 10(.946) translates into 10 + 9.46, which equals 19.46 If you round 19.46's tenth, it rounds up to 19.5. Thus we see that the Palatine Chainmail will have 19.5 Balance at the maximum upgrade (VII).