The short answer
Biological filtration is the work done by beneficial bacteria living on your filter media. These bacteria convert toxic fish waste — ammonia → nitrite → nitrate — turning deadly compounds into a far less harmful one you remove with water changes. It’s invisible, needs no power of its own, and is the single most important thing keeping your fish alive.
The nitrogen cycle
Fish waste and uneaten food release ammonia, which is highly toxic. One group of bacteria converts it to nitrite — still toxic. A second group converts nitrite to nitrate, which is relatively safe at low levels. This chain is the nitrogen cycle, and it runs continuously once your filter is established.
Nitrate is where biology stops — no bacteria remove it in a normal tank. That’s why you still need water changes to export it. See what is a safe nitrate level for an aquarium.
Where the bacteria live
They colonise every surface, but especially the porous biological media — ceramic rings, sintered glass, bio-balls — whose vast internal surface area houses billions of them. Mechanical media, substrate and decor host colonies too, but bio media is purpose-built for it. Read what is aquarium filter media for how the layers fit together.
Building and protecting it
A new filter has no bacteria — you grow the colony by cycling the tank before adding fish. The full method is in how to cycle an aquarium, and how do I set up a new aquarium filter covers the install. To keep biology healthy long-term, clean gently — see how to clean an aquarium filter and the aquarium filters hub.