By adding a few drops of water to a whisky, you can open up different, new and subtle flavours that you previously had not experienced. This is especially true when drinking cask strength whiskies that have higher alcohol levels.
With cask strength whisky the alcohol and resulting burning in your mouth can overpower even the most prominent flavours. By adding some water, this dilutes the alcohol and reduces its effect, giving both the prominent and more subtle flavours a chance to shine.
Imagine drinking a fruit cordial or concentrate without any water and then with water – it is essentially the same idea. How much water you then add is entirely dependent on your taste.