The reason why removing the top most bud, called the apical bud, works to promote lateral branching, is because the apical bud releases a hormone called indo acetic acid or IAA that is spread down the shoot to all lower buds causing them to either stop all growth, or at least to grow very slowly. This is accomplished by IAA inhibiting the growth hormon cytokinin. By removing the apical bud, the IAA's signal stops, thus the growth hormone cytokinin is no longer inhibited, therefore new lateral growth will quickly begin.