What is Nitrogen Cycle in Pond Filtration?

It is the process in which beneficial bacteria becomes established in your pond's filtration system and will effectively help in the conversion of toxic Ammonia generated by the fishes urine and excreta into non-toxic Nitrates.
The cycle begins when the fish eat the food and excrete ammonia.
The bacteria present in the biological filter media called Nitrosomonas eats the ammonia and excretes Nitrite. Both Ammonia and Nitrite is toxic to fish and hence needs to be removed from the water.
Then another type of Bacteria called the Nitrobacter in the filter media eats this Nitrite and releases Nitrate which is not harmful to fishes. Nitrate is also a fertilizer for plants.
This entire cycle then repeats itself upon completion.