vegetative bud on the side of a stem (contrast with terminal bud).

Merriam-Webster Online Dictionary
lateral bud (noun)
a bud that develops in the axil between a petiole and a stem
lateral bud (Wikipedia)

The axillary bud (or lateral bud) is an embryonic or organogenic shoot located in the axil of a leaf. Each bud has the potential to form shoots, and may be specialized in producing either vegetative shoots (stems and branches) or reproductive shoots (flowers). Once formed, a bud may remain dormant for some time, or it may form a shoot immediately.

The axillary buds are highlighted in yellow.
Axillary buds are located at the intersection of the leaf and stem of a plant.
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