Sump/fuge is basically the filtration system for the tank.
Three types of filtration: Biological, Mechanical, and Chemical.
Biological, a refugium will allow you to have a deep sand bed for nitrification....letting bacteria eat the waste in the tank, which means it breaks down ammonia. Being that you have a deep sand bed in the refugium, its not needed for the display. Live rock is also used here, this way you can have little or no live rock in your display but able to utilize the benifits of it. My lfs has a display with fish only, lr isn't in the display but down under it.
Mechanical, this is a type of filtration that traps wastes like left over food, fish poop, ect. you can use a sponge to trap this, i am in the process of getting a new tank up....not sure how i will take advantage of this type of filtration. any suggestions? thanks.
Chemical filtration, carbon and protein skimming....carbon helps with smell and yellowing of water....skimming is another way to reduce waste in the water.
just the basics, i reckon.
A fuge also adds to the tank volume. a 75 gallone tank 20 gallon fuge, 95 gallons total, more water the better. easier to maintain when problems arise.