If you have a wayland session on your computer, you don't want to hit ctrl-alt-8 to switch over to an X session running that single application, and then switch back and forth to wayland to use every other program. It would be nice if there was a X server that worked as a wayland client and could put the X-only application on your wayland desktop. That's Xwayland.
* For a better explanation on ditching X, and what Wayland is: see this talk from one of the X dudes working on Wayland http://www.youtube.com/watch?v=RIctzAQOe44
XQuartz is for running X11 applications inside Quartz (Mac OS X's window server/compositor), XWayland is for running X11 applications inside a window server/compositor that uses the Wayland protocol.
(N.B graphics are run as a server in Linux, you send requests to the server and it places you graphics on the screen (if applicable))
Edit: Can't seem to reply to child, but Mir isn't really a credible competitor (See: http://aseigo.blogspot.com/2014/03/more-on-why-display-serve... . Unfortunately Mir seems to be mostly NIH; everyone else is cooperating on Wayland.)
