noun

• (chiefly Southern US) A creek or stream which flows into a larger river.
  "branch water"
• (geometry) One of the portions of a curve that extends outwards to an indefinitely great distance.
  "the branches of a hyperbola"
• (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.
• (nautical) A certificate given by Trinity House to a pilot qualified to take navigational control of a ship in British waters.

verb

• (intransitive) To arise from the trunk or a larger branch of a tree.
• (intransitive) To produce branches.
  "The tree throve and branched so heavily that the windows of Lower West and the Doll's Flat were darkened."
• (ambitransitive) To (cause to) divide into separate parts or subdivisions.
• (intransitive, computing) To jump to a different location in a program, especially as the result of a conditional statement.