The Foc's'le refers to the upper deck of a sailing ship forward of the foremast, or the forward part of a ship in the days of sail. The US Navy still calls the forward most deck of the ship the forecastle out of tradition.
The Foc's'le of the ship houses the anchoring and mooring equipment for the destroyer. Heavy chains stored in a chain locker below decks lead up to the ship's two anchors secured in openings called hawsepipes. Two devices called pelican hooks hold the anchors in place in these hawsepipes. The anchor is raised and lowered by an electric hydraulic hoist called the anchor windlass that is controlled either by the on deck control station or from within the Windlass Equipment Room below. The black cylinder shaped object in the first photo shows both the capstan and wildcat. The capstan, or upper portion, is utilized for gripping and handling the destroyers mooring lines while the lower wildcat is used to move the anchor chain. In case of failure, the brass hand wheel adjacent to the capstan/wildcat is the brake that can be used to drop the anchors.
Some items on the Foc's'le were manual tools just like in the days of sail. Dual cylindrical protusions coming up from the deck were known as bitts that are used for securing mooring lines while the lines were protected from chafing by the use of openings along the ships gunnels (area along outside of ship) known as a chock.
Giving this deck area its power was the twin 5"38 caliber gun mount that could reach ranges between 8-10 miles and was a very effective and accurate weapon.