What exactly does the spec “PCIe 3.0 x16 slot (x4)” mean?

16x is physical slot size, that is capable of wiring up to 16 PCIe lanes, but on your motherboard that slot has only 4 lanes connected to it.

For the former slot with 16x or 8x/8x that means that when only one slot is occupied – it will get all 16 lanes, but when two slots are used – these 16 lanes will be divided by them.

This happens because CPUs have limited PCIe lanes count. To wire more lanes CPU need to have more pins in socket, more layers and copper on the motherboard etc. This is more expensive and most of buyers will not use more than 1-2 PCIe devices anyway.
Thus for some applications where these lanes are actually needed – one will have to install a top-tier server CPU with lots of cores that may not actually be used.