(noun)
something that is in an incompletely developed state, such as a partially-open flower, a projection from a simple organism that eventually forms a new individual, or an outgrowth from a complex organism that eventually forms an organ or appendage;
e.g. He broke off a bud of a red rose from the bush. The tadpole suffered a limb bud injury.
(noun)
a close friend, a partner or companion, a buddy;
e.g. He is my best bud and I trust him completely.
(verb)
to form a bud as an initial stage of the development of some structure, used to describe plant or animal behavior/growth;
e.g. You can see the trees starting to bud, which means that spring is coming.