Aquarium Filters are used to clean your water.
Several filter types exist, those being:
Mechanical filters are generally used to remove free floating particles from water, these filters in most cases are the base for more intricate filter systems.
Tank water is forced through some fine filter media and the particles are then trapped in the filter media.
More often than not, this filter media is Floss, or a similar fine filter media.
Biological filters rely on different types of bacteria to convert Ammonia and Nitrite to the less poisonous Nitrate in your aquarium water.
The substances are created by fish wastes and uneaten food that decompose in the water.
The above mentioned bacteria needs time to grow and multiply in order to efficiently remove the contaminants.
Chemical Filters use a combination of resins to remove contaminants out of the aquarium water.
Several of these resins exist and are commercially available.
Most Filter Systems use a combination of the above three filters.
I personally prefer using a corner box filter.
These filters require some maintenance, but are robust and easy to work with.
Box filters use all three of the above mentioned filtration types.
The filter floss is used as both mechanical filtration and as a breeding ground for the useful bacteria for your biological filter.
You add activated carbon and / or chemical resins to clean the tank water chemically.
NB: When cleaning your box filter, never remove all of the filter floss.
You will be removing all the beneficial bacteria and thus killing your fish.