Any unit within 12" of the battle standard may retake a failed Break test. The unit is only allowed to retake this test once. 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, the general's Leadership and the opportunity to re-take a failed throw, mean that units near to the general and the battle standard will tend to hold their ground come what may.

Note that a battle standard allows a unit to retake a failed Break test - and only a Break test. A battle standard does not entitle a unit to retake any other Leadership test, such as a psychology test or a test to rally.