Cycling a fish tank is one of the processes a tank undergoes as it matures.
In its simplest terms, it's how toxic fish waste is converted to less toxic forms.
Ammonia --> nitrite --> nitrate.
Bacteria is responsible for this conversion, long believed but recently
challenged to be nitrosomas and nitrobacter.
This bacteria can be found in the air, or on aquatic plants.
Like it or not, with or without your help, your tank will cycle.
Ammonia is most toxic to fish; nitrite slightly less so,
as are high levels of nitrates in the long term.
See fishless cycling links for starting a new tank; once you have an established tank, you can swap out filter media and/or gravel to "jump start" a new tank. Nitrate levels are controlled by regular water changes, and tanks which are heavily planted (though these also need routine water changes).
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