This traps even more little bits of dirt, algae and other unwanted stuff that had floated through the other steps of treatment. By this time the water is getting sparkling clean and this step is often called polishing, like when you polish your car to make it sparkle.
This filtering method copies nature - rainwater seeping through the ground gets cleaned the same way.
There are other parts of the filtration process that also keep the filters and pipes clean as well as cleaning the water. These are Backwashing and Air Scouring.