Tap water and well water are filled with all sorts of materials which are toxic to humans and to aquarium fish. ie: lead, mercury, arsenic, chromium, pesticides, herbicides, industrial pollutants, gasoline, and many, many more as well as phosphates and nitrates which fuel algae growth.
Distilled water or natural spring water at your supermarket may also contain copper and lead or various minerals which are toxic to fish. They also cost from $.50 to $1.00 per gallon.
Reverse Osmosis water filters utilize a membrane, under pressure, which forces water to leave its pollutants on one side of the membrane and produces water free of dissolved solids on the other side. The type of membrane determines how much toxic material is filtered out. Cellulose Tri-Acetate (CTA) membranes have a removal rate of 88-94%, Thin Film Composite (TFC) membranes remove between 94-98% of dissolved solids, and Hi-S Membranes have higher removal rates, between 97.5-99%, and are especially adept at removing silicates.
Some areas of the country such as where I live in Austin, Texas, the water is very hard (pH of 8.5 to 10). It contains huge amounts of limestone which buffers against lowering the pH by "absorbing" the acid content of the water and allowing the pH to rise. Reverse Osmosis is a very effective way to take the calcium carbonate out of the water to get the pH down.
It's hard enough to get rid of phosphates, nitrates, silicates, and other algae nutrients. It's even worse to add them to the tank when you do a water change because your source water already contains them. If your water source is high in algae-producing excess nutrients, it won't matter how many water changes you do to get rid of them and the algae they foster. Reverse Osmosis is a highly effective way to remove those nutrients BEFORE you put them into your aquarium.
Although there is some water waste in this process, for most areas of the country, R/O is the only reasonable alternative to using expensive or polluted water. They will produce water for about $.005 per gallon and the membranes will last for 5,000 to 10,000 gallons of product water if properly cared for. That usually equates to years.
Of course, there is a little maintenance involved with a Reverse Osmosis Filter. The system must be flushed on a regular basis. Carbon and sediment filters should be changed about every 6 mos. Make sure that the water coming into the unit is not hot, as that can severely damage the membrane. About 70° - 77° is optimal. Water pressure should be about 65 Lbs psi.
Copper is highly toxic to invertebrates. Lead, is of course, toxic to everyone. Other pollutants can be damaging in myriad ways. However, the reverse osmosis removal of all those pollutants also removes the "good" minerals from the water. For this reason, you must add back the trace elements and essential minerals your tank inhabitants need to remain healthy. Most marine salt mixes already contain the necessary minerals. However, freshwater tanks will need to be "re-mineralized" to achieve the required pH and equilibrium.
Reverse Osmosis units are less expensive and require less frequent maintenance than DEION units which use catiion and anion exchange resin filters.