I'm trying to grasp R2 to R3 Tensors: What does the 3rd dimensional coordinate system represent?

piped.video/watch?v=f5liqUk0ZTw

I think I understand the rank one and rank two systems, but I’m not clear about what the 3rd represents on a Cartesian plane.

My mental model involves tying concepts to CAD design and assemblies. I am coming from FreeCAD where picking origins and designing everything on planes is critical.

The thing that I really don’t understand about tensors yet is how the origins are derived and relate with different objects in 3d space. I want to assume R3 relates to the origin but I am not sure.