This is a really interesting sustainable method for food growth and production. It combines traditional aquacutlures (cultivation of water animals as clams, fish, crayfish, prawns and so on, in the current case – in tanks) with hydroponics (rough explanation is plant cultivation in water) thus creating a symbiotic environment. The aquatic organisms accumulate many waste products that become toxic at one moment for the aquatic life, so these waste materials are transferred to a hydroponic system using water pump. At the hydroponic system the by-products are filtered out as vital nutrients. After that cleansed water returns back to the aquatic animals.
Aquaponic systems may vary greatly in size, you may assemble one in your backyard or you may walk through large commercial units. However, they use the same principle. It is interesting that this method has ancient roots and is known that Aztec cultivated agricultural islands on the water surface, known as Chinampas. It is considered by some people as the first form of aquaponics for agricultural use. Poly-cultural farming systems also existed in South China and Thailand who cultivated rice in flooded fields in combination with fish.
Future Farm Food and Fuel is based in Baldwin Wisconsin and built the largest aquaponic system in North America. This system is spread over 27 000 ft. and produces tons of lettuce, other plants and tilapia (fish). 
via:afuturefarm,wikipedia