I offer, here, some of what I've learned. Towards Understanding Nature's Filtering System. It carves out a path leaving sand and gravel along it's edges. As it twists and turns the water flows over and through the sand and gravel, mixing freely with oxygen, and mechanically filtering out particles. Beneficial bacteria, that thrive in oxygenated water, and other life forms attach themselves to the gravel and sand surfaces and work on the wastes of fish-manure and rotting vegetation.
Ammonia is converted to nitrites, then to nitrates, which are taken up by aquatic plants and algae.
The water flows clear and often drinkable. This is what we try to mimic. My First Wimpy Up-Flow Filter I cleaned out the bottom muck which was causing toxic gases to build up. The vinyl tube ran down this pipe and released water at the bottom. It made an improvement, but was totally inadequate.