A PCIe lane is a pair of high speed differential serial connections, one in each location. A link between devices can be and often is made up of multiple lanes for higher data rates. The data rates of individual lanes also varies by generation, roughly speaking one lane of Gen x provides about the same data rate as two lanes of Gen x-1.
On modern Intel systems some PCIe lanes are provided by the CPU directly, while others are provided by the PCH in the chipset. The link from CPU to chipset is similar to PCIe but there are differences in the details.
Motherboard vendors have to decide how to allocate the lanes provided by the CPU and PCH to the onboard devices and slots. They can and often do include signal switches to give the user some options but there is a limit to how much signal switching can be affordably implemented.
Intels "mainstream desktop" platforms currently have 16 lanes from the CPU plus up to 24 (depending on which chipset is selected) from the chipset. However the lanes from the chipset are limited by the total bandwidth available from the CPU to the chipset (roughly equivalent to PCIe 3.0 x4 IIRC).
16 lanes from the CPU and 24 from the chipset more than enough for a normal desktop or small server, you can put your graphics card on the 16 lanes from the CPU and then the lanes from the chipset plus the integrated controllers in the chipset are generally enough for storage, networking etc. Even with two GPUs 8 lanes per GPU is enough most of the time.
However when building a high end system with 3+GPUs (or possiblly two top of the lines GPUs), lots of fast storage and/or very fast network interfaces more lanes are desirable. If you want to give each device it's maximum possible capacity you are looking at 16 lanes per GPU,
So for those with higher end needs Intel has a high end desktop socket, currently LGA2066. This socket also covers single socket workstation/server systems, though it seems officially at least you can't use the workstation/server processors in most desktop boards.
Unfortunately while with previous generations of high end desktop the number of PCIe lanes and ram channels was fixed, with LGA2066 the number varies by the processor you select. A desktop LGA2066 CPU can have 16, 28 or 44 PCIe lanes.
This puts motherboard vendors in a tricky position, they have to decide how they will handle giving the true high end customers the full functionality of their CPU while deciding what to disable or throttle for those with lower-end CPUs. System builders in turn must carefully read the manuals for the motherboards to find out what the limitations are before buying.
Grabbing the manual for one of the cheaper X299 boards https://dlcdnets.asus.com/pub/ASUS/mb/LGA2066/TUF_X299_MARK2/E12906_TUF_X299_MARK2_UM_WEB.pdf shows that the main limitation is the x16 slots, On a 44 lane CPU all three slots are usable with two running in x16 mode and one running in x8 mode. On the other hand on a 28 lane CPU you get one x16 one x8 and one unusable and on a 16 lane CPU you only get one x16 or two x8.
Grabbing the manual for a high end X299 board https://dlcdnets.asus.com/pub/ASUS/mb/LGA2066/ROG_RAMPAGE_VI_EXTREME_OMEGA/E15119_ROG_RAMPAGE_VI_EXTREME_OMEGA_UM_V2_WEB.pdf it seems they have decided not to support the 16 lane parts at all. This board does let you use three GPUs on a 28 lane CPU, but the second m.2 slot and the u.2 connector are only available with 44 lane CPUs