Topology refers to the layout of edges and faces within a mesh. The topology of a mesh can affect many aspects of the final result, from proper deformations during animation to flickering polygons at render time. Proper topology can migitate errors, and make aspects of other processes like UV mapping and morphing much easier to accomplish when good practice is in play.
It is common to hear terms like “edge loops” when referring to topology and deformations. Edge loop placement as a practice must be well-understood when modeling for deformation animation.