[Woodstock]

In my own lamen's term...
Bioballs have huge amounts of surface area for oxygen loving nitrifying bacteria to thrive. Since most bioballs are located in a high flow area, there are enormous amounts of oxygen available and a strong water flow that supply never ending food (ammonia). In this situation, the first set of bacteria will quickly eat ammonia creating nitrItes as a byproduct. The second type of bacteria quickly consume nitrItes which create nitrAtes as a byproduct. This has completed the nitrifying part. But here is where it ends because the last type of de-nitrifying bacteria needed to consume the nitrAtes into harmless gas are not to be found in this bioball world. The reason is that they require low oxygen (anerobic) areas to live; such as porous live rock and in sand beds. So here you have thriving bacteria producing huge amounts of nitrAtes constantly into the water column.

On the other fin,
Porous rock and fine aragonite sand (deeper larger diameter substrates too) not only provide large surface area for the nitrifying bacteria to do their work but there are also anearobic areas deep in the rock and sand for the de-nitrifying - nitrAte eating bacteria to thrive. In this situation the de-nitrifying bacteria can easily 'grab' food (nitrAtes) from the first set of bacteria. The by-product of these wonderful denitrators is a simple nitrogen gas that floats to the surface.

So, in the first senario, the water is filled with nitrates that the de-nitrifying bacteria can not 'grab' as easily. In the second scene, the de-nitrifying bacteria are literally handed the nitrAtes from the neighboring nitrifying bacteria.