Deep Sand Bed (DSB)
The correct term should actually be a Deep Live Sand Bed (DLSB), because the sand bed can only operate properly if it is populated with appropriate sand-living organisms. But I'm jumping ahead of myself, so lets start at the beginning...
Aim of a DLSB
The aim of all filtration systems is to reduce potentially toxic biological waste produced by our tank inhabitants to less harmful, or even better - totally non-toxic, products. In our tanks the waste from our fish and corals, and uneaten food, is quickly converted to ammonia/ammonium (depending on pH), which is highly toxic even in very low concentration. Aerobic (oxygen loving) bacteria in the tank can fortunately convert this ammonium into less toxic nitrite, which other aerobic bacteria then further converts into nitrate. Although nitrate is not very toxic for fish, it does have the potential to cause massive algae blooms, and is still rather toxic to corals and other invertebrates. Unfortunately, this nitrate can only be further broken down by anaerobic bacteria, which only live in areas where the oxygen level is rather low (but not totally absent...).
Both the aerobic and anaerobic bacteria need two things in order to multiply - enough food (the waste products) and enough suitable substrate "living space" (the rock or sand). In our natural filtration systems, we use live rock and/or live sand to act as substrate for both the aerobic and anaerobic bacteria. Because of it's size, a given volume of fine sand has a much larger surface area than the same volume of rock, and can house much more bacteria than the rock - thus making a sand bed a *much* better filter substrate than live rock.
With good water flow in the tank, the surface of the sand bed (and live rock) continuously receives highly aerated water, and this water can slowly permeate into the sand bed (and into the interior of the live rock). This water is rich in oxygen, and readily supports a dense growth of aerobic bacteria which then uses the oxygen to convert the ammonium to nitrites and then to nitrates. During this process the oxygen is used up, and as the water moves further into the sand bed or rock it becomes more and more anaerobic (oxygen poor). At some depth, depending on the grading of the sand and the flow of water above the sand bed, the oxygen concentration in the water drops to a level where anaerobic bacteria can live and multiply, and where they can then convert the nitrates (which are in solution in the permeating water) into inert nitrogen gas.
As stated earlier, our anaerobic bacteria live in oxygen poor water - but importantly, they still need *some* oxygen. As a sand bed becomes deeper still, the concentration of oxygen can decrease to a level below where these anaerobic bacteria can live and multiply - this is the so-called anoxic region, and it is inhabited by anoxic bacteria. These bacteria "breathe" sulfur, and in even more anoxic regions they can actually "breathe" calcium (but the latter only occur at really great depths in the oceans, and I have never heard of them living in our tanks...). Despite the old-wives tales and "mythology", these anoxic bacteria are actually very beneficial to our systems, as they not only convert nitrate into nitrogen gas, they also convert toxic heavy metals into non-toxic (and less soluble) metal salts.
"OK", you may ask, "but what about the toxic hydrogen sulphide gas and black areas in the sand?" Well, hydrogen sulphide IS pretty toxic if released into the water in a large volume. Fortunately, when a DLSB is operating properly, this gas is used up again by some of the bacteria, and/or is continuously released into the water in very small quantities which is totally non-toxic. It is only when the sand bed is "stirred" by either the aquarist, or by a large "sand sifting" fish or other animal (which should not be kept in a DLSB tank in the first place...) that there is a chance of a toxic gas release.
Contrary to popular belief, the black areas in the sand are also NOT indications of hydrogen sulphide production. The H2S gas is colourless, and can not turn the sand black. The black/brown/darkly coloured areas are actually caused by the anoxic bacteria converting metals, such as manganese (black), iron (red/brown), etc. into harmless manganese oxide, iron oxide, etc.
Life in the DLSB
"Right, now what about the "Live" in the DLSB?" The deep sand bed needs a constant, but very light, water flow through it, from the surface right down to the deepest part of the bed. This is achieved by the "pumping" and "crawling" action of the sand-living organisms in the DLSB. A mature, well-operating DLSB has literally thousands (if not tens-of-thousands...) of sand-living creatures, ranging from large polychaete (bristle) worms all the way down to microscopic flat worms, amoebas (if there are salt-water amoebae??), etc. in every cubic centimeter of sand. All these "critters" continuously move around in the sand, and the larger worms also "pump" water through their bodies whilst feeding (or breathing), and although each individual movement is quite insignificant, the total movement of all the critters can displace (and circulate) a surprisingly large volume of water.
A second reason for needing sand-living organisms in our DLSB is that they EAT. The larger worms would eat fish excrement, left-over food, and other "waste". Their waste is then eaten by the smaller copepods, whose waste is in turn consumed by micro flat worms, then by the single-celled organisms such as the amoeba... and so it goes all the way down the food chain, until the "waste" has been converted into nice "bite-size" portions for the bacteria.
To summarize - a successful DLSB needs the following: Properly graded, fine sand with all the particles having smooth, rounded surfaces - in other words, a "natural" sand such as real sea sand, river sand, etc. and NOT crushed sand (which have sharp edges due to the crushing process...). A total depth of between 75mm and 300mm, with the most recommended depth being between about 100mm - 150mm. A proper "seeding" with either live rock, or preferably live sand imported from a reef with many of it's critters. It is also a good idea to swap small amounts of sand with other aquarists, as this can increase the bio-diversity in the sand. Good water movement over the surface of the sand bed. No sand sifting fish or other creatures, and NO siphoning or stirring of the sand bed by the aquarist.
This has only just "skimmed" the surface of having a successful DLSB, but I hope that it has been of some use in clarifying this very interesting subject.