Topology is a term used in 3D graphics to describe how a mesh is sculpted and the overall cleanliness of the polygons. Essentially it comes down to using polygons correctly and not wastefully, ensuring they are readable, ensuring they are optimised and ensuring there are enough for objects to bend.
By using good topology;
- The mesh is easier to read
- The mesh flows correctly to the shape of the object
- The mesh can use less expensive polygons
- The mesh is easier to unwrap for texturing
- More polygons in the right places will ensure natural movement and bending of polygons
- Less wasted resources
- Something boxy does not need as many triangles as something organic as the shapes are easier to define, so polygons can be spared.
- Models design with animation in mind will work correctly.
- Shapes are correct, contours flow together.
Here is an example from clevermusings.com of good vs bad topology. As you can see the polygons on the left model are poorly placed and do not flow very well, whereas the model on the right is clean and uses polygons correctly to fit the shape of the face without resorting to using more polygons to fill in the gaps.