A compositor is a program responsible for displaying program windows and things like the desktop on your PC. On Linux, the compositor is just a program that starts when the system starts. There are multiple desktop environments available, like Plasma or Gnome, each comes with their own compositor, you can choose which you want to use.
Wayland is a protocol that the programs use to communicate with the compositor. Everyone decided to use Wayland, because if each compositor had their own protocol it would be silly, eg some programs would work only on Plasma or Gnome.
It’s a replacement for a much older X11, which could no longer keep up with requirements of modern apps.
You never hear anything about compositors on Windows or Mac because there’s only one available, you can’t choose.
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