A Segment is an edge that exists between two vertices. A line consists of one segment; a spline curve will often have many segments. There will always be one less segment per vertex-count in any line or curve.
As with vertices, it may be possible to have two segments occupying the same space in your mesh; this can happen in mesh editing, or especially with data that comes from DCC sources outside of the application. Such cases will typically cause trouble, and you should use the optimize tool to deal with the situation. You can verify this condition by using the select tool (with select visible only disabled) and rectangle select the suspected edge. You can use your viewport statistics option to determine if more than one edge has been selected. If so, you will need to melt, weld, optimize or actually delete the edge manually. If you cannot directly isolate the offending edge, delete your selection, and rebuild with Stitch & Sew or a similar tool.