(biology) The formation of an outgrowth from an organism, and is capable of developing into a new individual; gemmation.
(general) That is beginning to develop; the state of producing buds.
Budding is a common process in plants and fungi. It also occurs in certain animals, particularly the Hydra (sponges). In sponges, the outgrowth (bud) stays attached permanently while in fungi the bud stays for a while, and then detaches to grow fully as a new individual. Budding is a form of asexual reproduction since the process results in the formation of new individual but is a clone of the primary organism.