A DSB can go in either the main tank or a sump, though when putting it in the tank you are taking up a lot of display room (most DSB need around 6" to work effectively).
A plenum is a space at the bottom of a DSB. This appears to be very useful (perhaps a requisite?) on large DSB (think in the order of 3 or more feet deep) but seem to neither help nor hinder in smaller home aquaria situations [taken from the WWM site].
A refugium is an area away from the main display tank (sometimes a part of the sump, other times - as with my tanks - a separate tank from the sump or display) in which you can cultivate things that you don't want/wouldn't survive in the main tank. The two most common aims of a refugium (or fuge for short) are to have a decent colony of amphipods and copepods, or to grow a form of macroalgae (or indeed both in one).