The Z-height is exactly what it sounds like: the motion of the extruder or build plate in the Z direction. Getting the Z-height correct on a print can actually be more time consuming than thought and will almost always cause more hiccups than issues in the XY axis.
Just as with leveling the build plate, the Z-height needs to be correct in order for a print to start, not warp, not get clogged, and to overall finish properly.
When using a printer that does not have precise auto bed leveling and a way to automatically find the proper Z-height, which most do not, you will need to tweak the distance between the extruder and the Z-endstop. This can be done by homing your device and then tweaking with the screw that can adjust the distance between the extruder and the endstop.
Build Plate Expansion
When materials are heated they will expand from their normal size. This can be seen in both heat creep in the Barrel Cooling section as well as the effects of shrinking when cooling in the Warping section. The same is true for the glass build plate you are printing on.
When heating a bed to 110° celsius you are bound to make the glass expand a bit. This expansion will cause the build plate to be slightly closer to the nozzle than when cold. This is why it is best to determine the Z-height while the bed is heated to the temperature you expect to print at. Once this expansion is recognized, you can add G-Code to your slicer profile for that particular material with a Z-offset. This offset will cause the extruder to rise, or bed to lower, based on the amount of expansion.
Quality and Nozzle Size
As mentioned in the Quality Options section, when we say quality we mean the height of each layer as well as the nozzle size. When printing in fine quality of around 100 microns and with a nozzle smaller than .4mm in diameter, getting the proper Z-height can become quite a headache. The smaller the nozzle and the lower the layer heights, the more precise that the Z-height has to be. Printing at 400 micron layer heights on a .6mm nozzle is far easier to hone the Z-height than fine quality prints. So not only do high quality prints require more print time, but they require more labor as well.