Point of Balance
A: To be honest, I am shocked that you have given me a haircutting/styling term that I have never heard used. While balance is an important factor in cutting and styling the hair, I have never heard the term "point of balance" in connection with haircutting.
It may also (and is more likely to) refer to a point on the head used to ensure evenness in the haircut. Such as the points used in cutting long hairstyles where two locks of hair from similar positions on each side of the head are pulled to the point in a central location to ensure that the lengths created on each side of the head are in balance and even.
I am sorry to be unable to give you a definitive answer, but I do suggest that you review the source where you saw the term used and check for contextual definitions. If you are a student of cosmetology, you will want to ask your instructor since the source of the term is likely one of your texts.
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See also:
Hairstyling terms and definitions
What is the definition of Break Points in a haircut?
