All the devices on each floor are connected to a single floor-level switch. This is typically referred to as the access layer, in which the attached devices are hooked into a wider network. Often, the individual links between devices and the floor-level switches are 10Mbps Ethernet.
The floor-level switches are in turn connected into a second layer of switches (via Links 1, 2, and 3). The Links 1, 2, and 3 are often 1Gbps Ethernet (or GigE). This middle tier of switches acts as an aggregation layer, bringing all the connected elements together. This is sometimes called the distribution layer, and these devices can be connected to a third switch. The latter is the core layer. Again, the bandwidth of the links to the core switch is of the order of several Gbps.
Why have three network layers? The main reason is flexibility and ease of upgrade. The floor-level elements (computers and PBX, on floor 3) are isolated from the other two switch layers. If more devices are added to a given floor, any effect this hardware addition might have on the other equipment layers is minimized. This use of hardware layering is more generally referred to in computer science as separation of concerns and reflects the move away from monolithic arrangements. In fact, the emerging discipline of software architecture makes extensive use of this concept. You might say it's "the joy of separation!"