Cycling is the process your tank goes though as it builds up the necessary bacteria to help break down the fish waste in the water.
If you just pop fish into the tank, as they produce waste the bacteria start to grow. However this taks a while to happen. Usually the toxin levels rise high enough in the tank before the cycle properly kicks in such that some fish die or have health issues.
A fishless cycle as described in the top of this forum is the process of growing that necessary bacteria before putting your fish in. Its considered the humane way to do it.
