External filters, sometimes called canister filters, sit outside the aquarium below the water level (e.g. in a cabinet)
Water from the aquarium is drawn into the canister via a gravity siphon and pumped back into the aquarium by a water pump situated in the 'head' of the canister. As the water passes through the canister it is directed through a series of compartments that may contain mechanical, biological, or chemical filtration media.
The large size of the canister in comparison to filters that sit inside the aquarium, allow a much greater amount of media to be used and hence, provide better filtration.
Additional space also allows the option of adding specific medias, such as phosphate removers to the filter if and when required.
External filters are more expensive than other forms of filtration but have noticeable benefits and also require less maintenance.