Topological

Topography is the study of forms. focused on the surface elements. in the context of 3D modeling Its a type of editing that directly modifies the surface of a 3D form. This is in contrast to Boundary Representation modeling which modifies the equations that define a enclosed volume.

In layman's terms, usually Topological modeling is used for organic flowing shapes, and B-REP Modeling is used for production work and or Hard Surface Modeling.

Blender is a common example of a Topographic modeling program, while fusion360 or solidworks would primarily be Boundary Representation modelers.

In topological modeling, a decision needs to be made fairly early on; Quads or Triangles. Most modelers insist on quads being superior, but there are good cases for both.

Historically Triangles have been used. This largely is due to memory optimization. A triangle defines a plane, and can be defined using only 3 points.

A Quad can represent MANY different surfaces depending on the curvature. It requires more information to properly define a shape using quads, but the shape is much smoother. This is why modelers tend to prefer them. They contain much better surface information, instead of a relatively low poly collection of planes, you can define surfaces with known curvature, which makes renders, shaders, and other quality focused elements run better.

Additionally Triangles are harder to subdivide. The "flow" of a surface is much easier to parse/understand intuitively when the surface is a quad.

You can Split a quad by drawing two lines from adjacent mid points.