Sorry for the length of this response... if you've got insomnia, reading this post will certainly help:
Just like pH is a measure of the ratio of positive hydrogen ions to the number of negative hydroxy (OH) ions in your tank, ORP is a measure of the ratio of molecules that receive electrons (oxidize) versus the number of molecules that donate electrons (reduce). Why should we care about oxidizers and reducers? Well, in our bodies, oxidizers (some of which are called free radicals) are a bad thing... they damage cells and cause brain damage (just had to talk a little about the brain!). Therefore we take substances that act to reduce these oxidizers (Vitamin C and Vitamin E for example are anti-oxidants).
The best example of an oxidizer in your aquarium is O2 (oxygen), which is a weak oxidizer, and if you inject ozone (O3), that's a strong oxidizer. Deep in your sand bed where there's little to no oxygen, you'll find sulfate, which is a reducer. You want to have a reducing environment deep in your sand bed, because that's where anaerobic (oxygen hating) bacteria grow... it is these bacteria that convert nitrates into nitrogen gas (the little bubbles you see in your sand bed). That's a major method of exporting nitrogenous waste out of your tank: the nitrogen bubbles that rise to the surface and get released into the atmosphere.
Now organic waste (ammonium, nitrates/nitrites, protein waste) in your water are all reducers. You can see why you'd want to keep these reducers to a minimum. Ammonium ions are toxic to animal life, and while nitrates and nitrites are fairly harmless to animals, they are good fertilizer for nuisance algae.
When we place an ORP electrode into the water to measure water quality, the battle between the number of oxidizers and the number of reducers in the water takes place at the metal surface of the ORP electrode, and this exchange of positive and negative charges creates a voltage (the ORP or oxidation reduction potential). The higher the voltage, the more oxidizers, and the greater the water quality (less waste products). Ocean water has an ORP of about 400 mV (millivolts); aquarists that monitor ORP strive to keep ORP at about 375 - 450 mV. If you have really good aquarium technique, your ORP is probably already sufficiently high. Among the things that contribute to good technique include 1. good protein skimming to remove waste, 2. lots of live rock and perhaps a deep sand bed to provide substrate for anaerobic bacteria to eliminate nitrates, 3. perhaps growing macroalgae in a refugium to absorb nitrates, 4. a phosban reactor to absorb phosphates -another waste product and an algal fertilizer- 5. not an extreme number of livestock for the volume of water 6. no overfeeding, 7. sufficient crabs and snails to graze down nuisance algae. Not everybody does all of these - for example, you can be successful with a bare bottom tank, but there's no denying that all of these things help raise water quality.
It has been suggested that ozone helps break down organic waste and facilitates waste removal by protein skimmers. Several years back I noticed my water was a bit yellowish (I could see the color in the white bucket that I use for water changes). At that time I found that my nitrates were at about 30, so I got a better protein skimmer, I started growing chaetomorpha in a refugium, and I started injecting ozone. Now my nitrates are undetectable and my water is colorless, and nuisance algal growth is no longer a problem.
We use an ozone controller to measure and set the level of ORP that is desirable, so that the ozone generator doesn't go unchecked and inject too much ozone into the tank. Very high levels of ozone can actually harm marine life.
A warning, if you decide to inject ozone, you've got to make sure that before the ozone gas escapes into the air in your house, you pass it across a carbon filter... breathing high levels of ozone is not healthy (remember we don't want free radicals in our brain!!! - everything comes down to neuroscience!).
My apologies for the length of the above manuscript! Must have lapsed into professor mode. Hope it helps.
Jay