What would happen if the tips of the stem is cut off?
If the tip of growing stem is cut off, it will cause discharge of auxinhormone concentrated at tip to distribute in axillary buds which will promote branching or leaf growth.
Normally, when apical bud is present, the tendancy of auxin to discharge down is less. So, such practice is always performed in gardening to promote leaf and branch growth. This tendancy of auxin to remain at growing tip in presence of apical budis called apical dominance.
So, if you cut tip of stem, it will break apical dominance.