Deep sand bed is a take off from the plenum system, minus the egg-crate. The sand is live and a thickness bed of 4-6" is necessary for it to work properly. The sand is seeded with detrivores [cleanup crew or reef janitors which is the common names used]. Basically these are substrate-living creatures ranging from inverts like crabs to starfish. They can also be gobies or even a wrasse. These creatures keep the sand clean and turned-over, or, if you're a gardener like me, you can call it "tilling"
They also cleanup the detritus that falls into the sand bed. Using powerheads within the tank, you keep the water circulating and oxgenated. The sandbed, because it is sand and deep, helps to complete the nitrogen cycle and riding your tank of nitrates [something that other filtration systems like wet-dry does not do].
With the plenum, you have a similiar concept, except, because the anaerobic bacteria is produced beneath the egg crate, you don't need the detrivores to run your system.
This is a pretty simple explanation, but it sounded like you kinda need it simple at this point.
I would suggest that you read up on both systems and decide what is best. Use the search feature on this bullitin board and type in plenum and or DSB. The web, also, is loaded with info.
[ May 30, 2001: Message edited by: Beth ]