Empty water jugs were obtained in Pirate events in previous years. They are in circulation throughout Nexus and are not difficult to obtain.
Empty water jugs become Water jugs by filling them with water. You do this in the Water Pool in north Kugnae, at the coordinates 42, 28 and 30, 30 (above the Warrior Guild). Simply drop the Empty water jug into the water, and it will immediately be in your inventory as "Water jug."
Water jugs are used for Cheffing Noodles, and are also a requirement for the Staff of Elements quest.