A Sponge Filter is basically an air driven non-mechanical filter. Usually it is a sponge in the shape of a cylinder with a tube in the middle, an airstone is put down the tube, the rising bubbles draw water through the sponge thereby creating a flow through the sponge. The sponge acts as a biological (bacteria colonize the sponge) and mechanical filter.
There often used on breeder tanks because with mechanical filters there is the danger the fry will get sucked up by the filter. Also they're very cheap.