Short answers, pulled from the story.
A water clock, also called a clepsydra, is a timepiece that measures time by the regulated flow of liquid into or out of a vessel. The word clepsydra comes from the Greek meaning "water thief." Two main types exist: inflow clocks, in which a marked container fills over time, and outflow clocks, in which a filled container slowly drains.
The oldest water clock with surviving physical evidence dates to between 1417 and 1379 BC, from the reign of the Egyptian pharaoh Amenhotep III. It was found in the Precinct of Amun-Re at Karnak and took the form of a stone vessel with sloping sides and twelve columns of interior markings, one for each month of the year.
Egyptian priests used outflow water clocks to determine the time at night so that temple rites and sacrifices could be performed at the correct hour. The stone vessels had twelve columns of markings corresponding to the twelve months, accounting for seasonal variation in the length of the night hours.
Al-Jazari's castle clock, described in his 1206 treatise, was a water-powered astronomical clock about eleven feet high that some scholars consider an early example of a programmable analog computer. It displayed the zodiac and solar and lunar orbits, operated five musician automata via a water-wheel-driven camshaft, and could be reprogrammed to adjust for the changing lengths of day and night throughout the year.
The Borugak Jagyeongnu, built by Chang Yongsil in 1434 for Sejong the Great, was the first hydro-mechanically engineered dual-time clock in the history of horology. It used three wooden jack figures to strike the hours automatically, eliminating the need for human attendants, and employed a signal conversion device called the pangmok to announce discrete digital time while measuring continuous analog time.
Water viscosity changes with temperature, causing the flow rate through fine nozzles to vary. A temperature shift of one degree Celsius can alter viscosity by about two percent, meaning a water clock could gain or lose roughly half an hour per day if the temperature changed by just one degree. Ancient water clocks compensated by being reset daily against a sundial, which kept cumulative error manageable.
Water clocks were replaced in Europe around 1300 by the more accurate verge escapement mechanical clock. Before that point, the water clock had been among the most commonly used timekeeping devices for millennia across many civilizations.