A refugium is a portion of the water system that is connected but protected from the main display tank to allow macro algae and other macro filters to grow and develop, to allow planktonic and other feeder animals a place to repopulate and to provide space for biological filters, both macro and micro.
Primarily you will run a refugium for a few reasons
1. Micro-Biological filtration – The addition of extra live rock and sand into your refugium can add more capacity for the bacteria needed to convert ammonia into nitrate and if set up correctly, nitrate reduction.
2. Micro-Biological Natural Nitrate Reduction(NNR) – the addition of a Deep Sand Bed (DSB) and Live Rock can greatly reduce the amount of nitrates in your water column if managed properly
3. Macro Biological Filtration – Most notably Macro Algae vegetative filters (a big ball o' chaeto) will take nutrients out of the water column so nuisance algae are unable to use it. Sponges in a cryptic zone also would perform this function. As would several types of sessile animals. Once it grows to an unreasonable size you just pull some of it out and use it for fertilizer or trade with a friend, or roll it around a penny and give it to your enemies.
a. This is the most common use for a refugium. Nutrient export. You grow something and it uses nutrients to grow. Then you harshly yank it out or cut it off at the knees. Such is the cycle of life.
b. Remember that the nutrients are sequestered in macro until actually removed. They are just sitting there, waiting. For instance, if you grow ulva (one of my favorite macros) and feed it to a tang all the nutrients are back in your system. This isn't a bad thing but just something to consider.
4. Growing Food – Not only can you grow tasty macro's for your herbivorous fish friends but a refugium can provide a perfect environment to grow out various types of phyto and zooplankton.
a. This use of a refugium is one of the best in my opinion. There is currently a lot of research in this area but it is turning out that our corals really like to constantly eat. Not get a blast of food 3x a day or once every other day or what have you. A refugium can take the excess nutrients from your feedings and store them in the form of plankton that your corals, other invertebrates and fish can eat at their leisure. I also personally like the idea of a complete food chain within my tank and a refugium is really the only way to get close to that ideal.