The answer is that cruise ships always have access to fresh water that's obtained through several different techniques. For instance, some of the more modern and sizable cruise ships produce their own fresh water onboard via a desalination plant.

Yes, modern cruise ships have highly sophisticated "running water" systems that provide potable (drinking) water, hot showers, and functional sewage systems for thousands of passengers and crew members simultaneously. Because a ship cannot carry enough fresh water for a week-long voyage for 5,000 people, it essentially acts as a floating utility plant. Most of the water is produced onboard through two primary methods: Flash Evaporation (using the heat from the ship's engines to boil and distill seawater) and Reverse Osmosis (forcing seawater through extremely fine membranes to remove salt and impurities). This water is then mineralized and chlorinated to ensure it meets or exceeds the standards set by the World Health Organization and the U.S. Public Health Service. The water you find in your cabin's sink and shower is perfectly safe to drink, though some passengers prefer the taste of bottled water due to the slight "processed" flavor of desalinated water. Additionally, cruise ships utilize "grey water" (from sinks and showers) and "black water" (from toilets), which are treated in advanced onboard wastewater treatment plants before being discharged into the ocean under strict environmental regulations.