You've got several parts to your question.
Those parts are represented by the red, blue, and green arrows I've added to the drawing:
The blue part references what's between the layers where there's no copper.
PCBs are manuafactured from sheets of fiberglass matts and epoxy. Each layer is a premade sheet of fiberglass and epoxy with a sheet of (thin) copper on the top and bottom of the sheet.
The copper is etched to make the traces on the top and bottom of the layer.
When a multilayer PCB is assembled, the fabricator stacks up several of those sheets and lines them up carefully so that all the traces and other details line up.
There is a thin coat of epoxy between the layers. The whole stack is put under pressure (clamped flat together) until the epoxy is cured (hardens) so that the stack will stay together.
Between the layers is (at most) a very thin layer of epoxy. The fiberglass is "mashed" into the open areas around the copper by the pressure. Any open areas where the fiberglass can't reach (closest around the traces) will be filled with epoxy.
The red arrows indicate the "ribs" where the vias go through each layer.
Vias are made by drilling holes through the finished stack after the epoxy has set. The vias are then plated with copper. The copper plating in the holes joins all the copper layers together.
The PCB design software will include "rings" of copper on each layer to make the noted "ribs." The assembly process doesn't leave little gaps for the copper plating to spread out and make the "ribs." The "ribs" must be in the etched copper layer. When the through holes are plated, the rings specified by the design software are joined to the plated hole to make the "ribs."
The line indicated by the green arrow is somewhat misleading. That line appears to mark the boundary between the plating that make the through hole and the copper plating on the surface of a layer of fiberglass. The line would more properly be in the place marked in purple (just to the left of the green arrow.)
Speculation about the "ribs."
I don't know that any manufacturer requires adding the ribs. As far as I can tell, they are added by the PCB design software when placing the vias.
The Eurocircuits guidelines for making PCBs specificall says to remove the pads on any inner layer that you don't want connected to the through hole plating. That means the "ribs" aren't a required part of the manufacturing process.
Eurocircuits has a nice series on the construction of PCBs, describing the individual manufacturing steps. Each section in the series has a description with pictures and a video of the process.
To answer the additional question posted in the comments, the plating looks like "B" in the image below:
The "rings" in "A" are on the fiberglass layers. The plating goes inside the hole and over the surface of the top and bottom layers of the stack.