What it will do depends pretty heavily on what you put into it. If you just have water, nothing's going to happen.
But let's answer your second question first - Yes. There is absolutely a correlation to tank versus refugium sizes. A 10 gallon refugium will never be able to handle the full nutrient export of a 90 gallon tank. But that being said, it can
assist in nutrient export. Mark Callahan has a good overview on the size question here:
Refugiums in a Saltwater Tank: Viable Nutrient Control or Just a Safe Harbor?
Now, back to the first question. What stuff do you want in your refugium?
Macroalgae - Assists in nitrate and phosphate export. Conventional wisdom says that whatever is growing in your refugium won't be growing in your DT. While that's not always the case, having a dedicated area of growth that is specific to phosphates certainly can't hurt. As I eluded to earlier, I also use my refugium to grow macros that I provide to my fish as a source of fresh food.
Sand - Deep sand beds are (in my ever so humble opinion) the only sand worth doing in a refugium. Just like a DSB in a display, the mixture of aerobic and anaerobic bacteria can help to break down nutrients. However, just like in a DT, a remote DSB holds some dangers such as releasing hydrogen sulfide if they are disturbed.
Mud - STATED TO: Naturally replenish trace elements, allow for removal of skimmer from the system.
Mangroves - Look really cool. Not especially efficient at nutrient export. I've heard that you need 1 mangrove per gallon of water volume to effectively export nitrates.
Rock - Added biological filtration, just like the rock in your display. However, rock is also a great breeding grounds for copepods and amphipods, both of which are prime food sources for many fish such as wrasses, dragonets and others. I also tend to keep small rubble pieces in my refugium that I use to mount corals. I just pluck one out, use super glue + epoxy and then place it in the DT.
For more on this, there's a great resource over at ReefCleaners. I don't agree with everything that they say, but they walk through some of the more in-depth portions of which algae to use, etc.
http://www.reefcleaners.org/stocking-the-sump-refugium