Hard water is any water containing an appreciable quantity of dissolved minerals. Soft water is treated water in which the only cation (positively charged ion) is sodium. The minerals in water give it a characteristic taste. Some natural mineral waters are highly sought for their flavor and the health benefits they may confer. Soft water, on the other hand, may taste salty and may not be suitable for drinking.
If soft water tastes bad, then why might you use a water softener? The answer is that extremely hard water may shorten the life of plumbing and lessen the effectiveness of certain cleaning agents. When hard water is heated, the carbonates precipitate out of solution, forming scale in pipes and tea kettles. In addition to narrowing and potentially clogging the pipes, scale prevents efficient heat transfer, so a water heater with scale will have to use a lot of energy to give you hot water. Soap is less effective in hard water because its reacts to form the calcium or magnesium salt of the organic acid of the soap. These salts are insoluble and form grayish soap scum, but no cleansing lather. Detergents, on the other hand, lather in both hard and soft water. Calcium and magnesium salts of the detergent's organic acids form, but these salts are soluble in water.
Hard water can be softened (have its minerals removed) by treating it with lime or by passing it over an ion exchange resin. The ion exchange resins are complex sodium salts. Water flows over the resin surface, dissolving the sodium. The calcium, magnesium, and other cations precipitate onto the resin surface. Sodium goes into the water, but the other cations stay with the resin. Very hard water will end up tasting saltier than water that had fewer dissolved minerals.
Most of the ions have been removed in soft water, but sodium and various anions (negatively charged ions) still remain. Water can be deionized by using a resin that replaces cations with hydrogen and anions with hydroxide. With this type of resin, the cations stick to the resin and the hydrogen and hydroxide that are released combine to form pure water.