Balance points are marks and notches that help align adjoining pattern pieces when constructing a garment.
In this image there are notch points in (1) the Bodice Back side seam and in (2) the shoulder front.
The side seam notch is a balance point that will line up with the dart in the Front Bodice piece.
When the front and back are lined up at the side seam, you can see that the notch (balance point) in the back lines up with the dart on the front piece.
This must true whether you line them up from the armhole (image 2) or the waist (image 3).