Segments were removed in October 2007 with the introduction of API v0.5 to simplify the data model.
Segments connected two nodes and should always have been connected to a way or an area (if not they were "unwayed segments"). Segments could be a part of multiple ways or areas, much like how relation can have the same children as other relations today.
Now (after October 2007), the word "segment" is used to mean a straight section of a way between two nodes. This is similar to its previous meaning, but a segment manifests itself within node and way definitions rather than being an actual data primitive. To be clearer it may be better to refer to them as "way segments".