Cycling (fish-in or otherwise) is the process of allowing a colony of bacteria to grow in the filter. These bacteria process ammonia, which fish release from their gills, and which is produced as fish poop, uneaten food, or any other organic waste in the tank breaks down. Ammonia is very deadly, so it can turn water very toxic very quickly if not dealt with.
These bacteria themselves produce nitrIte, which isn't as toxic as ammonia, but still not great - it binds to hemoglobin and effectively suffocates fish, no matter how much oxygen is available. The second part of the cycle promotes the growth of a second type of bacteria, which process nitrIte into nitrAte, which is harmless in controlled amounts - generally, water quality will go bad in other ways like a pH crash before nitrate itself becomes an issue.
With both ammonia and nitrIte, any amount over 0 is bad, anything over 0.25 ppm is cause for immediate concern, and anything over 0.50 ppm can cause immediate harm to most fish. Prolonged exposure even to trace levels is stressful, but even short term exposure to elevated levels can cause permanent gill damage and black chemical burns on the fish's skin.
Now, specifically for fishless cycling, we use a purified ammonia source (or failing that, rotting fish food or cocktail shrimp - there's a nigh-legendary story floating around about one man who successfully did one using measured doses of his own urine) to simulate a fish load during this process. There's no fish in the tank to worry about, so we can let water quality decline as far as it will without worry. When fish are added to an uncycled tank, the water quality has to be closely monitored, and water changes have to be done to protect the fish from their own waste products. Some people have come to this forum with ammonia in excess of 8.0 ppm within a week of setting up an uncycled tank. These levels are fatal within hours to some fish, and few of the hardiest fish in the hobby can last more than a day or two exposed to them.
Bottled water is pretty bad for keeping fish. There's two main types of bottled water: The kind with way too much mineral content, and the kind with almost none. In the latter case, it tends to create a very unstable pH. The pH in the tank generally wants to drop - acidic byproducts of the nitrogen cycle bacteria eat away at the carbonate hardness almost always present in tapwater - when this hardness is eliminated, the pH can drop very far, very quickly.
Except for a short list of highly sensitive species, and breeding of soft water fish, a pH anywhere from 6 to 8 is ok. Fish will tolerate a stable pH well outside their ideal range much better than they'll tolerate a fluctuating pH in their ideal range. Most of the time, dechlorinated tapwater is ideal. In the few cases where hardness or pH has to be tinkered with, purified water and pH altering chemicals are generally inadvisable, as both tend to create pH swings, rather than the stable pH you're aiming for.
