What is retopology?
Topology is preserving geometrical objects structure under deformations for maximum efficiency and functionality, without holes, passing through itself, tearing or gluing. The fundamentals of topology are continuous, compact, and connected.
Retopology in 3D modeling are the act of recreate an object topology in a 3D software.
Why is good topology important?
As 3D modeler, we want to preserve object details as much as possible (shape, shading, texture, etc.) under deformations for its intended purposes (mainly animation).
What is considered good topology?
A topology is considered good if its structure able to compact intended shape and details for animation. Example of a bad topology and a good topology:


the topology in first picture will deform badly in animation and have too much poly which isn’t effective.
The topology in second picture will deform according to human face muscle and retaining its intended shape.