What is the greeter?

When I was troubleshooting an Xorg problem, I came across solutions telling me to set the greeter such as:

greeter-session=unity-greeter

But I am unable to understand:

• what a greeter is to begin with, and
• why can a misconfigured greeter cause Xorg to run in low graphics mode?

A greeter is a graphical login interface. It's also often called the login screen.

Greeters are provided by the system's display manager. This wikipedia article on LightDM, the display manager written by Canonical for Ubuntu systems, lists greeters that can be used with LightDM, such as the Unity greeter. Not all current versions and flavors of Ubuntu use LightDM; for example, those that have GNOME as their desktop environment use GDM.

The display manager is responsible for starting the graphics server, Xorg (or, these days, sometimes Wayland). After that, it presents the greeter. If the greeter can't be started for some reason, such as misconfiguration, you won't be able to log into your system graphically.

I think your question is referring to this answer about a bug in LightDM causing the low graphics mode message to confusingly appear when the greeter can't be found. This bug was fixed long ago. If you are getting the low graphics mode error now, it's more likely to be a graphics driver issue.