Auxins are hormones produced in the apical meristems (cells at the tip of stems and roots.) These hormones stimulate or inhibit cell lengthening.
Movement of auxins to the shaded side of the plant cause cells on that side to elongate (lengthen) and that causes the plant to bend towards the light.
Auxins also regulate cell division in the side branches of a plant. High levels of auxin in the apical meristems keep side branches from forming. So what would happen to the shape of a plant if you snip off the tips?