Topology refers to how the components of a mesh are connected to one another. Topology is not the same thing as shape – it is possible for multiple models to have identical shapes but different topology, as you can see in the following image:
In the preceding image, the hand model on the left has very messy topology. It's made up of triangles that are randomly scattered around its surface. There are no clear patterns in the arrangement of the topology, so it requires approximately 7,000 polygons to represent the shape of the hand. This is not very efficient, but even worse is the fact that the surface of this model looks jagged. Just like a crumpled piece of paper, it will be nearly impossible for the surface of this model to look smooth again once it's got all...