Cycling is the natural process of taking bad chemicals and bacteria( Ammonia and Nitrites) and converting them to safer bacteria in your tank. The whole process is to keep your fish happy and safe. You start with Ammonia, from excess food and fish waste and as it breaks down it becomes Ammonia, In turn the Ammonia is the kept in check by bacteria called Nitrites. As the Nitrites flourish you will have another bacteria come along (Nitrates) which keeps them in check. Nitrates are safer for fish and they are dealt with during your regular water changes.
So basically the cycling process takes the bad stuff that is harmful to your fish and converts it to safer stuff
Les