I'm not an expert in this field whatsoever, but I found this interesting read on Wikipedia:
Plant physiologists have identified four different stages the plant goes through after the apex is removed (Stages I-IV). The four stages are referred to as
1. lateral bud formation,
2. "imposition of inhibition" (apical dominance),
3. initiation of lateral bud outgrowth following decapitation, and
4. elongation and development of the lateral bud into a branch.
These stages can also be defined by the hormones that are regulating the process which are as follows: Stage I, cytokinin promoted, causing the lateral bud to form since cytokinin plays a role in cell division; Stage II, auxin is promoted, resulting in apical dominance ("imposition of inhibition"); Stage III, cytokinin released resulting in outward growth of the lateral bud; and Stage IV, auxin is decreased and gibberellic acid is promoted which results in cell division, enabling the bud or branch to continue outward growth.
More simply stated, lateral bud formation is inhibited by the shoot apical meristem (SAM). The lateral bud primordium (from which the lateral bud develops) is located below SAM. The shoot tip rising from the SAM inhibits the growth of the lateral bud by repressing auxin.
When the shoot is cut off, the lateral bud begins to lengthen which is mediated by a release of cytokinin. Once the apical dominance has been lifted from the plant, elongation and lateral growth is promoted and the lateral buds grow into new branches. When lateral bud formation prevents the plant from growing upward, it is undergoing lateral dominance. Often, lateral dominance can be triggered by decapitating the SAM or artificially decreasing the concentration of auxin in plant tissues.
Hope this helps