A tank cycle is when the tank has bacteria to take care of the fish's waste.
You need a filter to have a cycle for your fish tank. Your water "cycles" around and cleans the water via filter...
The fish poop, and the poop makes ammonia. Ammonia is converted to nitrIte (harmful..) then it is converted to NirAte (least harmful) which is removed by your partial water changes.
To cycle the tank, add household ammonia for a fishless cycle. It's much nicer..