What is axillary bud?
It is a spot between the stem and the petiole. It is a spot that can have primary growth (like growing a new structure), as opposed to only secondary growth (get bigger, like a leaf growing in size or a stem widening). It is inhibited by the apical meristem (the thing that normally starts all structures, initiating all primary growth) and so, once the apical meristem moves on, the inhibition weakens and allows the axillary bud to activate.