If you're a standard Ubuntu user you probably won't notice much, because it's the developers getting gray hairs from X. They work around all the shitty problems so it works for you, just like users felt IE6 worked fine.
The main issue is how rendering is done on modern applications/desktops:
1. The client draws everything into a bitmap using its own tools
2. The client passes it via X to the compositor, which puts it together
3. The compositor passes it via X to the hardware, which draws it
So X does not do a whole lot anymore, and what it does it does poorly. Lots of blocking calls, poor versioning (per client, not per bind), poor synchronization (tearing), hardware overlays don't mix well with regular compositing, support for multiple monitors and input devices with hotplugging, global hotkeys/media keys, conflicts like modal window and screensaver both wanting to be on top and so on.
So what is it X did, that Wayland doesn't do anymore:
1. Help you draw the application (use Qt/Gtk/vwWidgets/OpenGL instead)
2. Draw the application somewhere else, assuming it wasn't just passed as a complete bitmap. In that case remote X and Wayland over RDP will perform similarly.
And though it's not directly part of the protocol, you're likely to see a revisit of client vs server-side decorations since Weston - the reference implementation - only support CSD. Basically, who draws the borders, title and buttons of the window. Mobile applications make this more interesting since you often don't want to dedicate the screen space, but you still want to be able to move/minimize/close/kill frozen applications through hot corners and such. But primarily it's a technology migration.