Topology

When researching topology I found it originally referred to a branch of mathematics that concerned itself with spatial properties that would be subject to distortion or motion. This helped make it quite clear that facial topology is all about looking at the deformation and movement of a face.
Topology in the animating sense is all about following the actual anatomy of a face, the facial structure and muscles to see how a face would realistically distort and move.

This picture here for example shows how topology works with the muscles in a face to show how that face would move realistically.

Topology seems to be applicable to both 2D faces and 3D. However on 2D images topology is only put on there for reference for 3D modelling.

This face has lines showing the topology of the polygons used. It shows how the polygons should distort in order to create a realistic looking opening and closing mouth.
Topological lines seem to be focused around circling the eyes and mouth. This makes sense as these areas in the face have the most movement and would require more attention in how they would move in a 3D polygonal model.