Answer:
a line segment for which direction matters
Explanation:
You want to know what "directed line segment" means.
Line segment
A line segment is defined by its two endpoints. A segment between points A and B can be named either of AB or BA. Such a segment has no associated direction. Neither point is necessarily the beginning point or the end point.
Directed line segment
A directed line segment has a direction associated with it. Often, you will see this when asked find a point partway along a line segment. Unless it is a midpoint, the direction of travel matters: 1/3 of the distance from A to B is different from 1/3 of the distance from B to A.
One or more directed line segments can specify a route from a beginning point to an ending point.
One point of a directed line segment is the beginning of the segment; the other point is the end point. When the segment is named, the beginning point is listed first.
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Additional comment
Directed segments are often seen as edges of a graph. The attachment shows an example. This graph shows no way to get to node 1 from any other, and no way to get from node 2 to any other.
On a map, they may signify one-way streets.
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