Although there are several types of aquarium filter, they all serve at least two functions - mechanical and biological filtration of the aquarium water.
The primary, mechanical, function is to remove solid particles of debris that would otherwise cloud the water. The debris is trapped in the filter media which is usually a plastic sponge material or, in the case of undergravel filtration systems, the gravel itself.
Over a period of time, beneficial bacteria build up on the filter media and the filter begins to perform its second, or biological, function.
Most filters (other than undergravel types) also provide compartments for other filter materials in addition to the normal plastic sponge. These compartments are used to hold carbon, zeolite or other special additives and are used to provide chemical filtration to remove toxic compounds which are actually dissolved in the water and which, therefore, cannot be removed with normal mechanical or biological filtration. In a balanced, healthy aquarium, chemical filtration is not normally required but it is sometimes used to remove traces of medication which may have been added to the water to control an outbreak of disease.
Filters are manufactured in various sizes to suit the volume of the aquarium in which it is to be used. It is generally recommended to choose a filter which has a 'throughput' which filters at least three to four times the capacity of your tank per hour. Although an excessively large filter will do no harm, it may cause problems with turbulence which some of your fish - and your plants - may dislike. Slight turbulence is desirable, though, as it helps to maintain an even temperature throughout the tank and helps to sweep debris into the filter inlet. Turbulence on the water's surface is also desirable as the vital exchange of oxygen into the water can only take place at the surface and the turbulence increases the surface area and, therefore, the oxygen intake of the water.
Tanks longer than, say, 36" (90 cms) can usefully use two smaller filters. This can help keep turbulence acceptably low whilst providing good circulation. New fishkeepers often find that their initial choice of tank proves to be a little small and 'upgrade' to a larger one. By using two smaller filters, the original one can still have a useful life. The only penalty is a little extra maintenance!