Nitrogen cycle in a fish tank
The first few weeks of a new aquarium are crucial. Before buying fish we must prepare a "house" for them by establishing the necessary biology for a healthy life. Fish wastes, leftover food, and all other organic matter that accumulate in a tank don't disappear like magic. They are decomposed by microorganisms, often resulting in toxic substances. There are also creatures that transform these decomposed substances into new compounds that can be used by other creatures.
In a new tank, nitrifying bacteria are rare. They will grow over 2-6 weeks (‘cycling’ the tank), then the tank is ready for the fish. They will grow if there is a source of organic matter in the tank (e.g. some plants or a pinch of flake food).
When you ‘cycle’ a tank you are taking it through the nitrogen cycle. Basically, fish eat food, digest it, and then output the waste, which takes the form of ammonia among other things. Decaying organic matter that may be in the tank also produces ammonia. Ammonia is deadly to fish, that’s why they get it out of their system.
There are bacteria that will ‘eat’ the ammonia and turn it into nitrite, which can also harm your fish. Another kind of bacteria will then ‘eat’ the nitrite and turn it into nitrate, which is less harmful to your fish. If you have plants in your tank they will absorb some of the nitrates. If not, doing a partial water change will help to reduce the amount of nitrate to a tolerable level. So, in order to get the deadly ammonia and nitrite out of your tank, you need these beneficial bacteria. They will grow naturally in your tank over time but it can take weeks to get a good population going.
Summarise from postings by Vany Devos, Tiago Beltrão and Marcos Avila and David Ducharme http://www.aquahobby.com/articles/e_ciclo.php