Refugiums have a seperate chamber from the main tank but shares the water column and this give us more water volume, which leads to water chemistry stablity.
They may contain live rock and/or live sand which gives us more natural biological filtration.
They can be used with or without a lighting system, but this would depend on what you design as a refugium.
Refugiums allow uninhibited organism development free of usual grazers, thus you can grow pods, shrimp and worms in an enviroment free from molestation.
They can provide a place for seperating some of the animals that you keep that wind up fighting, or a temp home for some critters that you need to get out of the main display.
They provide a method of cultivation of food for your system ie.. phyto, pods, macro algea if you have a tang that would eat them.
You can grow macro algaes for natural filtration and food
It is possible to even use for breeding fish.
I find that I can place my bags of animals that I need to acclimate right into the fuge and run a drip line to them, so I don't need to drip into a bucket, though I do need to empty water from the bag to the bucket.
With a reverse lighting schedual you can wind up with a much more stable pH by using a fuge.
My fuge is a 55 gallon with chaetomorpha algae and a 4.5 to 5 inch DSB, and some live rock, even a few corals that I had to move, or I will hold them there for trade or to go to the LFS with them for credit.