well at its simplest design, its a tray of water, with a grate that allows algea to cling to and grow. the tray is then filled with water from the tank that contains all the nitrogen in varies cycles, produced by the fish in the tank. this water is held in the tray for a given amount of time, then returned to the tank, via sump or pump.
instead of having bacteria break down the nitrogen as we all are custom to doing, this system uses algea to do it all, in the ocean most of the filtration is done in this manner. to keep the algea properous a light is used to satisfy the basic demands of the plant while it sucks the nitrogen out of the water. a system that is functing properly can be more effective than a regular bacteria fueled system and has some benefits over a bacterial filter, algea overgrowth will need to be scraped from the trays to keep the filter is constant growth, this overgrowth can be prepared and fed to fish in the tank, it oxygenates the aquarium water, and is restistent to medications aimed at killing off bacteria (bacteria that causes ick, hole in the head disease, etc)
thats a crude explanation of the system, i am sure ashdavid or czcz can go into the more detail. or people can always google it, we do live in the information age.