Whisky is by definition a strong alcohol (between 40% and 60%). This high alcohol rate is difficult to appreciate by people who are not used to it. This can be considered as an aggression to the papilla's. Adding some fresh water softens the aggressive character of a strong alcohol.
But, even for people who are used to drink strong alcohols, adding a drop of fresh water will open up new horizons. Adding a drop of water will provoke a chemical reaction, freeing the fragrances. The whisky will "open" itself.
In the case of a "cask strength" (generally round 60%), adding water will make it possible to taste the whisky at different alcohol rates. The drinker is entitled to determine the best alcohol rate for himself. When he decides it has reached the ideal alcohol rate, he just can stop adding water.