The hard deposits left behind after hard water dries are called lime scales.
These minerals are difficult to remove, and can even cause chemical reactions that make cleaning products less effective. Permanent damage can be left on glass.
In some cases, mineral deposits can become so bad that there is a chemical change that permanently damages the material. For example, if you have a glass shower door with a white, cloudy residue that never seems to come off completely, those stains may be permanent because the chemicals have etched the glass.