Bead filters are closed (pressure) vessels filled with millions of small plastic beads. These beads float and therefore provide a means of mechanical filtration and the enormous surface of these beads provides the biological filtration.
Mechanical filtration: the beads float in a closed vessel and are packed very close to each other. The pressure of the pump makes the water flow upward through the beads.
The small dirt particles will stick to the bead pack. The longer the filter is active, the more bio film there will be around the beads and therefore small particles can be filtered.
Biological filtration: the specific surface of the beads is about 1600m² per m³ (6 times more than a blue Japanese Mat), so the bio film layer around the beads is extremely useful nor nitrifying bacteria that consume vast amounts of ammonia, nitrites and nitrates.