I think most of us use the blind stitch (also called the blind hem stitch) because that is what we learned so it is easiest for us. With it, the thread is advanced in the fold of the binding. There are at least two other, equally good, invisible stitches that can be used for binding. The appliqué stitch, where the thread is advanced behind the fabric, and the ladder stitch, where the thread is advanced behind the fabric and in the fold.
Matching the thread color to the binding (or using a neutral for multicolored bindings), keeping the stitches as tiny and as close together as possible, and pulling the thread snugly enough to secure the stitches, yet not so tight as to pucker the binding all help to make hand stitching invisible.