A refugium is a separate area connected to the aquarium that generally contains macro algae, sand/aragonite, rubble rock and some sort of copopods, amphipods or small proliferating shrimp. The purpose is multi-functional.
If the refugium contains illuminated macro algae, as it grows it will strip out phosphates, silicates and nitrates. This is done by the macro algae sequestering the materials for growth. When the algae gets dense in the refugium you remove some of it thus removing the nutrients from the system. This will slow the growth of unwanted algae in the tank and help to maintain nitrates at a near zero value.
If a refugium is illuminated reverse of the aquarium it will effectively help reduce pH fluctuation. The reason for this is the macro algae utilizes the CO2 which is expelled through fish respiration and other sources during the night. If you have had a calcium reactor you would be aware that CO2 lowers the pH of the water as it is accumulated. This system utilizes the photosynthesis of the coral in the day and the macro algae at night to keep CO2 at constant levels.
If you have ever tried to keep copopod hunters (Mandarin Goby) you know that unless they convert to frozen it is hard to keep them long term. This is because they eat all of the small invertebrates in the tank and leave very few for breading. A refugium acts as a refuge for these small creatures and allows them to breed and then be re-introduced into the aquarium at a constant rate. The supply of small inverts is then kept at healthy levels thus making healthy fish and coral.
Hope this helps.