There are three types of filtration: biological, mechanical and chemical.
This site is an introductory site for fish keeping and a description of
these filtration types is beyond its scope.
However, filtration is a subject of importance. In short you will need
some sort of filtration to get rid of fish waste and uneaten food.
Without filtration the water will become polluted with these things and
constant water changes will be needed. The other option is if your fish
are in an aquarium filled with live plants. In this case the plants will
take care of the filtration.
Plants are expensive and difficult to keep alive for beginners since they
require an understanding of soil and gravel types and a more detailed
explanation and understanding of the nitrogen cycle.
So you will most likely be needing a filter of some sorts. There are two
main types. Those which are placed in your aquarium, and those which are
outside of the aquarium.
The ones which are placed within are small and usually are made partly out
of sponges or a mixture of charcoal and cotton. They work with an
and pump which circulate water through the filtration material. The
advantages of these are they are small and cheap. However, they require a
little more work to clean.
The other type are filters which do not sit in the aquarium, but either
hang on the side, or sit on the ground. These use pumps to pump water
through their filtration materials and pour the water back into the
aquarium. These are easier to clean and filter more material, however,
they do cost more.
Whichever type of filter you get you should get something which will
filter all the water several times an hour. So if you have a 10 gallon
tank then a filter which does 80 gallons an hour is good enough. However
that filter will have a problem keeping up with 3 goldfish in a 30 gallon