A sponge filter is just an air line and a sponge. How it works is quite simple and there are many different designs. You have an airline that runs down the inside of a tube that is a little bigger than the airline itself. At the end of the tube you have a sponge. Now, when you turn the air pump on, it will push air through the airline, the air will come out of the end of the airline above the sponge and the bubbles will float up through the tube that the airline is in. What his does is pull water through the sponge, filtering the water.
You can also just take a piece of sponge/foam and put the end of the airline under it and turn it un allowing the air to travel through the sponge, this will also filter the water by drawing water through the sponge.
This is a very cheap filter, and if anything ever happened to your current power filter and you could not get it going for a couple of days, then this would be a good alternative in the meantime.
-FHM