Fish live in water, and their bodies contain water; the fish’s cells separate these two waters, but the cells are semi-permeable, which means the cell will permit the movement of water and certain non-polar molecules to pass through either way (called osmosis) but will prevent the passage of larger or charged molecules. The way the water moves is determined by the difference in concentrations between the two waters: water of higher concentration (more dense) will attempt to pass through to the water of lower concentration (less dense) until the two are equal. If the fish could not somehow control this natural flow, it would either rapidly dehydrate or explode. But fish are able to control this through osmoregulation, a complex series of chemical processes. The water moving in or out of the fish’s body will likely have a different pH, so another set of processes controls the function of regulating the pH of the fish’s blood (Muha, 2005). Both of these processes also affect the ability of the blood to carry oxygen, and this impacts many other functions including digestion, the immune system, and so on.
The kidneys primarily work to eliminate excess water, but another function is the conservation and reabsorption of essential salts. Both processes work to maintain a specific salt/water balance. This osmoregulation of bodily fluids requires a great amount of metabolic energy. So a high osmotic pressure (caused by elevated levels of TDS outside the fish’s natural range) will overwhelm the fish with excess water and overwork the kidneys, while a low osmotic pressure (caused by TDS levels below those of the fish’s natural range) will deprive the fish of the water needed for the kidney functions (Evans, 2004).
Water hardness is the measure of dissolved mineral salts in the water, a portion of the TDS (total dissolved solids). There are two basic types of hardness of importance to aquarists, termed general hardness (abbreviated GH) and carbonate hardness (abbreviated KH, from the German “karbon” [carbon]). The combined GH and KH is sometimes termed “total hardness,” but this is of less importance because the GH and KH individually impact the water in different ways. General Hardness is determined primarily by the minerals calcium and magnesium; GH is sometimes referred to as “permanent hardness” because it cannot be removed from water by boiling as can KH. Fish are directly impacted by GH and TDS; their growth, the transfer of nutrients and waste products through cell membranes, spawning (sperm transfer, egg fertility or hatching), and the proper functioning of internal organs such as the kidneys can all be affected.
Hard water species must have calcium and magnesium present in the water in order for their kidneys to function, and beyond that. They have no means of getting this except from the water entering their bodies. As this water passes through the kidneys, the process of osmoregulation determines how the water is processed. Mineral salts like the calcium are extracted by the kidneys. In hard water species these mineral salts are essential to the proper functioning of the internal processes that work continually to maintain the fish's equilibrium; without these minerals the fish slowly weakens and dies. In fishes evolved in soft water, the salts are "foreign substances" that the fish does not have the ability to deal with, simply because it was never designed to do so. Calcium builds up, blocking the kidneys, and the fish dies.
The fish's internal biological processes are governed by the environmental factors mentioned above. The fish must for example regulate the pH of its blood to equal that of the water in which it lives, ensure the tissues are fed, the immune system functions, etc. The fish's physiology depends upon factors determined by the environment. As soon as these factors are changed from what the fish is programmed and designed to use, it creates stress, but even more significantly, the fish must expend considerable energy attempting to "right" what is "wrong." And generally it cannot do this, at least not for long, or depending upon the degree of difference. This means the fish slowly weakens. Usually the severe failure of the immune system causes the fish to die from some disease or issue that it normally should have easily dealt with, but could not because of its weakened state. In all cases, should the fish somehow miraculously succeed in avoiding disease, it has been weakened to such a degree that it can no longer support life processes and it dies, prematurely. There are no external signs of any of this, until the fish dies. Necropsy (autopsy in animals) can determine exactly which process failed.