defination of a bud and budding 

A bud is a small protrusion (also known as a bleb), or daughter cell formed on the parent cell which gets detached from the parent and develops into a new individual.

Budding is a form of asexual reproduction and involves the formation of a new individual from a protrusion called the bud. It is very common in plants, yeasts, and lower level animals like Hydra.