In nautical usage the term "sheet" is applied to a rope or chain attached to the lower corners of a sail for the purpose of extension or change of direction. The connection in derivation with the root "shoot" is more clearly seen in "sheet-anchor", one that is kept in reserve, to be "shot" in case of emergency.
Fore-and-aft rigs comprise the vast majority of sailing vessels in use today, including effectively all dinghies and yachts. The sheet on a fore-and-aft sail controls the angle of the sail to the wind, and should be adjusted to keep the sail just filled. Most smaller boats use the Bermuda rig, which has two or three sets of sheets:
On the smallest boats, a sheet is often a simple line, pulled by hand; on larger boats, intermediate blocks are sometimes used to provide mechanical advantage. However, many blocks and their multiply reeved lines, particularly on headsails, have been replaced by single-line sheets trimmed by powerful winches.
Square-rigged vessels are much less common, and are usually large ships. Nevertheless, they too have sheets on the movable corners of their square sails. Unlike fore-and-aft sheets, though, square-rig sheets do not control the angle of the sails (which is performed using braces); instead, they are used to haul the corners of the sails from their stowed positions down towards the tip of the yard below. They are then not adjusted significantly while sailing until the sail is to be handed (put away) again. The lowest sails, the courses, are trimmed using the sheets as these sails are loose footed and are secured to yards only at the head.
The length of chain running diagonally up and right from the bottom-left of this picture to the upper of the two yards is the fore-lower-topsail sheet. Some of the lines on Prince William's larger sails are made of chain to handle the heavy loads while remaining flexible enough to pass through the various blocks on their route to the deck.