Left click and drag a box around the tiles you want to move. Then:
Click the left mouse button and drag the tiles to a new location. The place where the tiles were will be replaced with the background tile.
Click the right mouse button and drag the tiles to a new location. The place where the tiles were will remain unchanged, because the right mouse button created a copy of the selected tiles, which you moved to a different location.
Use left mouse button to move, right mouse button to copy.