Hardness of water refers to the amount of calcium and magnesium ions present in water. Hard water contains more calcium and magnesium ions and produces less lather with soap, while soft water contains less and produces more lather. There are two types of hardness: temporary hardness caused by carbonate and bicarbonate ions that can be removed by boiling, and permanent hardness caused by chloride and sulfate ions that cannot be removed by boiling and requires softening processes. Total hardness is determined through experimentation and is classified for different uses, with units that can be converted between measurements like parts per million (ppm) and grains per gallon (gpg).