Airplay mirroring with extended desktop: how to choose which apps end up on Apple TV?
When you switch from Mirroring to Extended Desktop


  To move open windows, or Applications, to the Apple TV display simply
  click and drag the window by the Title Bar to the left hand side of
  your display (keep dragging over the screen edge). As you do this the window will appear in a transparent
  view on the Apple TV display. Once the entire window is on the new
  display, it will become active and can be interacted with in your
  second workspace........


You can also use Mission control and just drag the allocations between the displays.

And the cmd left arrow