Other forms: branches; branched; branching
A branch can mean the "arm" of a tree, or any other kind of arm––a branch of a bank is a division of the bank.
Branch also works as a verb. If you play soccer every day after school and you want to "branch out" athletically, you might consider playing tennis. You might turn onto a little road that branches off a main one. A branch of a river is called a tributary.