Branch water
Branch water simply refers to plain water and the term is most commonly used when it is mixed with a liquor such as whiskey. This term originates from the Southern U.S. and commonly refers to water from a "branch" of a river, e.g. a stream. It also refers to water that was collected in a barrel under maple trees (that is, dripped from the branch) prevalent in Kentucky. The natural sugars from the maple leaves would give the water a delicate sweetness that complements Kentucky bourbon.
This term is generally used to distinguish the type of water, either when ordering a drink (meaning not soda water) or specifying origin (meaning not well water).
Branch water can also refer to water infused with buds or needles from an evergreen tree, which was used by Native Americans as a remedy for scurvy [1]. However, this term is not in common usage.
References
The American Heritage Dictionary of the English Language [2], Fourth Edition, 2000.