Budding is the formation of a new organism by the protrusion of part of another organism. This is very common in plants and fungi, but may be found in animal organisms as well, such as the Hydra. Usually, the protrusion stays attached to the primary organism for a while, before becoming free. The new organism is naturally genetically identical to the primary one (a clone). When yeast buds, one cell becomes two cells. When a sponge buds, a part of the parent sponge falls off and starts to grow into a new sponge. These are examples of asexual reproduction.
Budding is the process by which enveloped viruses acquire their external envelope, often as fragment of the host cell membrane, which bulges outwards and takes the virion inside. Because viruses are not alive, the Gag protein is essential for this process. Some viruses hijack the host cell proteins normally involved in endocytosis to facilitate this process.
This method helps the virus leave the cell without lysing the cell, thereby allowing the cellular machinery to produce more viruses.
The term budding is also applied to the process of embryonic differentiation in which new structures are formed by outgrowth from preexisting parts.