A Baggywrinkle is much like a cylinder-shaped "bristle brush" that can be installed to any shroud, stay, topping lift or lazy-jack. It works by creating a 'safe zone' against chafe... gently but firmly holding the sail off and away from the rigging.
On traditional sailing vessels (gaff rigs, schooners, tall ships, etc.) it's common to have multiple sets of baggywrinkles all throughout the standing and running rigging... anywhere that a sail might otherwise rub against wire, seizings, blocks, ratlines, etc.
Offshore cruising vessels sometimes use baggywrinkles too, because in many cases they provide better sail protection aloft than store-bought alternatives like spreader boots, shroud rollers or multiple layers of rigging tape. On a modern rig, they are frequently installed at the spreaders and aft lower shrouds to prevent mainsail chafe on a downwind run. Cutter rigged vessels might install them on standing backstays.
WHY MANILA ROPE?
Baggywrinkles are almost always made of manila rope fibers because manila provides the correct level of 'stiffness' to hold the sail off the rigging. Other types of rope could be used, but they are too soft to provide adequate protection.