It's a system combining aquaculture and hydroponics. You keep fish in a tub where they emit nutrients into the water. This is composed of algae, uneaten food and feces. Sounds yummy, huh? Well, in another container, more shallow but a wider surface area, you place gravel, sand or clay. Then you plant seeds in the medium. These can be anything from lettuce to tomatoes. There is a wide variety of plants that will thrive in this environment. You irrigate these plants with water pumped from the fish tank. The plants suck up all the wonderful nutrients from the water and then it is returned to the fish tank, cleaned and filtered. All you need to do once the whole thing is established is feed the fish. This system allows you to grow fish and edible veggies that use 1/10th of the water required and two to three times faster than earth-based vegetables. So you can grow more in a smaller space. If you set it up in a greenhouse you can continue this process year round. It is also reported that the quality of the veggies is much higher than their in-ground counterparts.
I personally haven't done it yet but I'm planning to just as soon as I can find answers to my questions.