The nitrogen cycle is a process of chemical transformations that occur through digestions in the aquarium.

Ammonia is produced by fish as a waste product of their digestive processes and as a result of the decay of other matter within the aquarium (such as excess food or dead fish)

Nitrites are produced by a colony of bacteria that establishes itself in the aquarium within two weeks of set-up. These bacteria process ammonia and produce the slightly less-toxic nitrites.

Nitrates are produced by a second colony of bacteria which establishes itself soon after the first colony. This colony processes nitrites into the relatively non-toxic nitrates.

Plants and algae in the aquarium consume the nitrates and produce oxygen and carbon dioxide.

While the nitrates may be "relatively" non-toxic, even with plants in the aquarium it is necessary to do periodic partial water changes. I have been doing 40% water changes once every two weeks for several months, and now that I've gone through a long string of diseases, I am going to return to doing 30% water changes every week to try for a more stable aquarium environment.