What is the purpose of running all the wires of a switch into another switch?

The kind of cabling you use for in-wall installation is often different to the wire you use in a conventional cable for patching.

A Patch panel is typically used as a place to terminate (connect) the in-wall cabling, with the other ends usually connected to wall sockets out in offices or classrooms. Since none of this wire moves, it isn't subject to wear and tear (metal fatigue) that occurs with flexible cables.

Patch cables are then used to connect the patch points to the actual network equipment. This allows for flexibility - patches can be changed to accommodate changing business (or technical) requirements, without touching the wires inside the walls.

The top device is not a switch, it's a patch panel :)

It's a patch panel, as others have stated -- however, there is one really awesome reason you'd do so if that had been a switch.