IMO a refugium is mostly often used as a place where you are growing things, cultivating things that may later be removed. This is different from the display tank, where you're goal may be to create a balanced sustained environment.
Most folks in the hobby with refugiums use them primarily to grow aquatic plants like Caulerpas. The caulerpas use nitrates, a bi-product of the feeding cycle in the display tank, to grow. So if you have a display tank and a working refugium, you can remove nitrates in two ways. First, water changes. Second, growing the caulerpa and trimming it back and removing the trimmings. The trimmings represent nitrates being removed from the system.
There are many other reasons and ways to have a refugium, but that is the most common.