ok, I am probably the worst person in the world to try to explain this stuff, but here goes and I know the other guys will jump in and fix my descriptions...
Essentially, it a tank like the above described one, another tank, half full of water (sump) sits underneath the main tank. It too, is usually drilled. A water pump, takes water from this smaller tank and shoves it up to the top tank, thereby making it "overflow" into the overflow boxes. The main tank has drilled holes inside these boxes and hose or pipe will run from the main tank, back into the sump. So you have one big water loop. This circulates the water. Most people put heaters, skimmers in the sump, to keep them out of sight. Also, some sumps are partitioned so that you can add more liverock and plants to help filter your water. When this is done, the sump becomes a "refugium".
Hopefully I have not confused you too much