If an edge on the surface boundary belongs to a triangle that slopes down toward that edge, then water flows off the surface all along that edge. A boundary segment is a connected sequence of such edges.
If a watershed has this type of drain target, it is called a boundary segment watershed.
In the following illustration, the edges p1-p2, p2-p3, and p3-p4 form a boundary segment.
Note: The "t" in the illustration indicates that the triangle was split between two watersheds because the water flowing across that triangle could go to either of two watersheds.