The following is from wikipedia:
"Branch water may refer to:
Water from a stream (a term primarily used in the southern United States)
Addition of plain water rather than soda water to a mixed drink (for example, "Bourbon and branch" refers to Bourbon whiskey with plain water)
When a whisky is ‘cut’ (i.e. watered down) prior to bottling, the water that is used is very important to the final product. The preferred source of water is called ’branch water’. Branch water comes directly from the stream that the distillery is built on, some companies even bottle this water, so that bar customers can further dilute their bourbon with the original bourbon water. This branch water starts its life in the underground limestone shelf that exists under most of Kentucky, and part of Tennessee. The limestone shelf acts as a natural filter for water that passes over it. Branch water is particular for its lack of character, with no traces of iron, or other minerals that would be harmful to the whisky making process."