If the downhill end of a channel edge is on the surface boundary, then water flowing through that channel continues off the surface. The boundary point is the lowest end of the channel.
If a watershed has this type of drain target, it is called a boundary point watershed.
In the following illustration, point p5 is a boundary point, the drain target of the channel p7-p6-p5:
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.