The rope you're speaking of is the mast rotation adjustment rope. The tighter you cleat it, the less your mast will be allowed to rotate and vise versa. Yes, you do let it move with the slack of the rope. The more slack you have the more the mast will be allowed to rotate. "Toward the side stays" means that the aft portion of your mast (where the mainsail track is) is pointed at the side stays, the wires that hold your mast up. Think of your mast as the leading edge of your sail and adjust it's rotation to conform with the shape (or foil) of your mainsail.
Quote:
More to the back for fuller sail and more toward the front for flatter sail
What ncmbm is referring to here is de-powering of the rig in heavy wind. "more to the back" would refer to less mast rotation, the aft of the mast pointing towards the stern of the boat and "more toward the front" refers to lots of rotation meaning the aft of the mast is pointing more towards the bows of the boat.
Tom