The purpose of cycling a tank is to get the aquarium into a stable state to house aquatic life. Many new aquarist get discourage in the beginning of this hobby because they don't understand the pitfalls of the new tank syndrome. So whats a new tank syndrome? Well to summarize its when an aquarium is newly started there is no biological bacteria in the aquarium to help with breaking down nitrate and ammonia that starts to build up. As fish and other animals start to lay waste into the aquarium the ammonia level rises.
Ammonia is number cause of fish deaths in a newly establish aquarium. The reason for this is that beneficial bacteria that is needed to break down ammonia into less toxic form is not present in a new aquarium. By cycling a tank means to let the aquarium start culturing these beneficial bacteria. So how do you get these beneficial bacteria growing? The way you get them to start growing in your aquarium is to put a small piece of table shrimp or you may purchase some ammonia starter and put that into the aquarium. Once there is a ammonia source the bacteria will start to grow and start consuming ammonia.
As the toxic ammonia starts to break down the aquarium will start to become habitable for life. So how can you tell if your tank is completely cycle? You will know when your tank is cycle is when you no longer can test for nitrate, nitrite and ammonia levels in your water. When these three parameters reaches zero is when the tank is finally cycle and ready for adding fishes into the aquarium.