Let me preface this by saying that I have none of the 3, but I wish I had them.
Overflow: small, blocked-off area which the water flows over the top, ususally thorugh a hole drilled in the bottom of the aquarium into the sump. That lets all that junk that usually floats around on the top of the water to be processed by the skimmer or other filtration equipment in the...
Sump: extra reservoir of water, usually below the tank, which the aquarium is connected to via overflow coming in and some kind of water pump going out. Its benefits include allowing for greater water volume, making a good place for unsightly equipment like heaters and skimmers, and a good place to put a...
Refugium: usually a part of the sump where certain types of macroalgae grow that take in nurtrients used by algae. The theory is to trim the macroalgae every so often to ''export'' those nutrients from the tank. Of course, a refugium needs to be lit, a subject which I know little about, since I don't have one and all.
I say I would like to have all of these things because 1) I'm having film algae problems, 2) I have a nice coating of slime on the top of the tank that my skimmer, even with the top-skimming-thingy, just can't get rid of, and 3) my skimmer and heater look ugly in the tank. Not having them saves money, but you may pay for it in tank-unsightlyness. _________ Prevent dihydrogen monoxide contamination in your aquarium: www.dhmo.org | 
