A typical use might be to set factor and units to 1.0 to offset primitives into positive Z (into the screen) and enable polygon offset for fill mode. Two passes are then made, once with the model's solid geometry and once again with the line geometry. Nearly edge-on filled polygons are pushed substantially away from the eyepoint, to minimize interference with the line geometry, while nearly planar polygons are drawn at least one depth buffer unit behind the line geometry.
Theoretically, you could draw fill mode normally and, line mode with -1 to offset them "out" of the screen/scene. +1 is moving them deeper.
glLineWidth also covers anti-aliasing