1. s. The woody part of a tree arising from the trunk and usually dividing.
2. s. Any of the parts of something that divides like the branch of a tree.
the branch of an antler, a chandelier, or a railway
3. s. (in particular) A creek or stream which flows into a larger river. (In the US, branch is a Southern US term; compare Ohio, Pennsylvania and West Virginia run, and New York and New England brook.)
4. s. (geometry) One of the portions of a curve that extends outwards to an indefinitely great distance.
the branches of a hyperbola
5. s. A location of an organization with several locations.
Our main branch is downtown, and we have branches in all major suburbs.
6. s. A line of family descent, in distinction from some other line or lines from the same stock; any descendant in such a line.
the English branch of a family
7. s. (Mormonism) A local congregation of the LDS Church that is not large enough to form a ward; see Wikipedia article on ward in LDS church.
8. s. An area in business or of knowledge, research.
9. s. (nautical) A certificate given by Trinity House to a pilot qualified to take navigational control of a ship in British waters.
10. s. (computer architecture) A sequence of code that is conditionally executed.
11. s. (computing) A group of related files in a source control system, including for example source code, build scripts, and media such as images.
12. s. (rail transport) A branch line.
13. v. (intransitive) To arise from the trunk or a larger branch of a tree.
14. v. (intransitive) To produce branches.
15. v. To (cause to) divide into separate parts or subdivisions.
16. v. (intransitive, computing) To jump to a different location in a program, especially as the result of a conditional statement.