All friendly units within 12" of the battle standard automatically re-roll failed. This rule ceases to apply while the battle standard is fleeing or if he is hiding at the back of a unit instead of fighting. Remember that you are only allowed to re-roll the dice once.
Note that the controlling player may not choose whether or not a unit is going to use the battle standard re-roll, but must always use it if the first test is failed.
If the General is within 12" of the unit as well, then it will also benefit from being able to use his Leadership value. These two factors combined, theand the opportunity to re-roll a failed Break test, mean that units near to the General and the battle standard will tend to hold their ground a lot more resolutely.
Note that a battle standard allows a unit to re-roll a failed Break test - and only a Break test. It does not entitle a unit to retake any other, such as a or a .