*The nitrogen cycle: The Reader's Digest Version*
In the air, on surfaces and all around are certain bacteria called nitrifiers. They're always looking for food; specifically nitrogenous waste. One way mother nature supplies that food is the waste produced by fish. Ammonia, a nitrogenous waste, in their respiration as well as their waste products. Those bacteria start colonising a fish tank when there is enough ammonia to eat. They eat the ammonia, and convert it to nitrite. Another bacteria shows up, eats the nitrites and convert it to nitrates.
Because the bacteria aren't in the tank initially (at least, not without the help of mature filter squeezings, gravel from a mature tank, Bio-Spira, etc), it takes em a while to build up decent size colonies. So initially the waste the fish produce isn't all converted cause there isn't enough bacteria to eat it. It winds up sitting in the tank poisoning your fish. Thats why we encourage folks to test for ammonia; its deadly and needs to be diluted (water changes). Less then .5
ppm is ok
IMHO.
Once theres enough ammonia eating bacteria, nitrites start showing up in the tests. Again, we encourage testing cause nitrites are also deadly and need to be diluted. Less then .5
ppm is ok (again)
IMHO.
Then once theres enough nitrites, the bacteria that eat them show up. They don't colonise the tank as quickly as the ammonia eating ones, so that stage may take a while longer then the initial ammonia reduction. Nitrates aren't a problem at low levels (40ppm or less) so the rush to water change isn't as pressing.
Basically, you need to test the waters to ensure you are not endangering your fish. And by doing those tests, you can see how the bacteria are doing colonising your tank. Once ammonia and nitrites no longer register on the tests, but only nitrates do, you know your tank now has a large enough colony of bacteria to deal with the nitrogenous wastes being produced in the tank.
One last thing. Because anything you add into the tank stays there (albeit in a different form *grin* like food becomes poo), you need to continue doing water changes even after the there's enough bacteria. The result of that cycle of ammonia to nitrite to nitrates ARE those levels of nitrates, as nothing eats it. Hence removing it by regular water changes.