Nuclear plants are built on the shores of lakes, rivers, and oceans because these bodies provide the large quantities of cooling water needed to handle the heat discharge. As energy is created in power plants, a significant amount of heat is produced. Water is utilized throughout the day to absorb this heat. Water is also utilized to cool down the equipment used in creating electricity. In the event of an accident, nuclear power plants need water to help remove the decay heat produced by the reactor core.
Coal burning power plants are located near water because the water is used to create energy. In these plants coal is burned in a boiler which heats water and produces steam. The steam flows into a turbine which spins, and produces electricity.
Both coal burning and nuclear power plants produce energy using steam turbines. large amount of water is required for producing steam for the steam turbine, and for condensing the steam released from the steam turbine outlets to increase the efficiency of turbine. Generally the power plants recirculate the water required for these purposes. Still a small percentage of water gets evaporated and need to be replaced. This small percentage of water also constitutes a large quantity.
Also the power plans may release the hot water from the condenser in the river and take fresh water from the river. In such power plants the water requirements is much greater. However, these days most of the power plants cool and reuse the water.