Why Work with Quads?
When you have a mesh based on quads it add a lot of benefits. The mesh becomes more regular and predictable. The grid structure that comes from quads provide meshes with directions of flow.
Tools can follow an edge and select loops in a predictable order.
Or they can select every opposite edge, making a ring selection.
UV mapping is also easier - the grid makes the mesh easier to map seamless texture mapping.

Working with Quads in SketchUp
When working with quad based meshes you quickly discover the need for quads where the vertices aren't coplanar.
In SketchUp this can be a challenge because SketchUp's Auto-Fold feature will break a quad into two triangles once it's vertices isn't coplanar any more.
To allow extensions to work with quads that are not coplanar they need to be able to determine which pair of triangles represent a quad. There is no official standard for this, but the de-facto standard is the QuadFace Tools type of quads.
The definition of a QuadFace Tools quad is that two triangles share an edge which is soft and smooth - with Cast Shadows turned off.
It is highly recommended that you also install QuadFace Tools to assist in creating quad based meshes for subdividing with SUbD. I is a core tool for creating ideal geometry that subdivide well.

Home page - https://evilsoftwareempire.com/subd/