Once pixels are selected, you can pick them up and rearrange them.
Drag inside the selection to lift the pixels off the layer and float them; click elsewhere or deselect to set them down.
Option-drag to move a copy, leaving the original in place.
Arrow keys nudge the selection 1 pixel; add Shift for 10 pixels. (Selection > Move Selection offers the same moves as menu commands.)
Press Delete (or choose Selection > Delete Selection) to clear the selected pixels to the eraser colour.
While a selection is active, the flip and rotate commands in the Canvas and Layer menus apply to the selection instead of the whole canvas or layer.