Well there are two kinds, the type that hang on the back of the tank, and the type that are drilled through the side or bottom of the tank. Both work the same way.
To explain it simply - ok, so if you fill up your tank then stop filling it, the water stops rising. Add water, the water rises. Now, say you punch a hole in the side of the tank. Once the rising water reaches that level, it stops rising. No matter how much water you pump in (to a point anyway), the water level will not get any higher, because its leaking all over your floor out of the hole in your tank.
Now, attach some plumbing to that hole and drain it down into a sump under the tank. So, when you keep adding water to the tank, it now drains into the sump. Water level in the tank still reaches a maximum level then starts overflowing out the hole and into the sump.
Now, instead of adding water from an outside source to get the tank to overflow, put a pump in your sump. The pump will pump water into the main tank, where the level will start to rise. Eventually, the water will rise up to the hole in the tank, and start overflowing back down into the sump. Now you have a system, water goes up and down, round and round. So, when you add water, its clear that the level in the tank always stays the same, so the level in the sump will go up. Evaporation has the opposite effect, the water level in the sump will drop, but the tank level will still remain the same.
A drilled tank just needs a hole in the side or bottom to drain through. A HOB overflow basically has two chambers connected by a syphon. One chamber on the inside of the tank, and one on the outside. So, since there is a syphon loop connecting them, if the water level in the inside chamber rises, the water level in the outer chamber rises. As soon as it gets to a certain point, the water in the outside chamber flows over a wall and down a drain, again returning to the sump.
As far as max flow rates, if I remember correctly A 1" bulkhead fitting will flow about 600gph. So obviously, larger tanks that require more flow will either use larger bulkheads, or more often, multiple overflows. My 55 and my 150 both use a single 1" overflow, simply because the 55 is a reef tank and needs very high turnover, and the 150 uses a wet/dry system so uses low turnover. The 55 is drilled and the 150 is a HOB, and both work equally well when properly designed. Both can be made to be almost silent. The only extra part needed for a HOB is usually a small powerhead with an airline connected to the syphon loop to suck out any air bubbles that develop. This is most peoples' concern about a HOB overflow box - if too much air gets into the syphon loop, it will stop overflowing. Then, the pump keeps pumping water into the tank, but its not overflowing so it keeps rising until it overflows over the top of the tank. I've been running a HOB overflow box for over a year now and have never had this problem, using the powerhead to keep it primed. Hopefully that clears up the basic mechanics of the idea.