Bio-filtration is the third type of filtration in the aquarium. Biological "filtration" extends the sense of "filtration" to include the varied uses made of dissolved substances by living organisms, hopefully by plants, but also by algae and mainly  by the mixed bacterial community that forms the basis of the biofilm that covers every permanently wet surface in the aquarium.
The "biological filter" operating throughout the aquarium takes ammonia and metabolizes it to harmless nitrate. Though that's just one aspect of the paths of energy and nutrients, it's more convenient to think of biological "filtration" in that context. So, though biological "filtration" is actually more essential to the success of your aquarium than mechanical filtration, I've treated material about biofiltration as part of the nitrogen cycle — and other cycles  —  in the "Nutrient cycles" folder.
You can learn a lot about bio-filtration in the aquarium by following some technological developments in the wastewater management industry. See the article "biofilter" at Wikipedia.