Hi jrdivagrl,
I'm sure there are a couple of threads in this forum that cover your question.
But it's a slow lazy Saturday ...
On open circuit diving with compressed air you take a breath, your body metabolizes about 4-5% of the 21% of oxygen, and expells the rest of it, together with the inert nitrogen and some carbon dioxide (CO2) which the body produces, into the water. All those noisy bubbles that head for the surface, and not a very efficient use of breathing gas.
The basic idea behind a rebreather is that the gas moves through a loop and get used again. That loop needs to have at least one flexible container that will expand when you exhale, and contract when you inhale, a breathing bag or counterlung.
In order to remove the CO2 that is produced chemicals are in the loop that absorb the CO2 and produce moisture and heat. That process is called scrubbing, the container that holds the chemical is the scrubber. You breath warm and moist gas, not cold and dry as delivered from a second stage.
As the body metabolizes the O2 in the gas, new O2 needs to be added. This can be done in different ways, either by using a premixed gas, usually with a higher O2 content than Air (EAN = Enriched Air Nitrox), or by adding pure O2 and mixing it with the gas in the loop. This process of adding the gas can either be done manually or by electronics with a manual back-up for emergencies.
All these bits are usually connected by large diameter breathing hoses. They need to be that wide to help assure the diver gets all the gas he needs with the least amount of effort. That's because the loop is at ambient pressure so you can breathe at all.
The rebreathers that use premixed Nitrox usually add a bit more than the diver should need, as the metabolism depends on various factors such as workload, fitness, temperatures etc.. These rebreathers are called semi-closed, as they expell some gas into the water.
The ones that mix pure O2 into the loop waste even less as only the used O2 is replenished. These rebreathers have O2 sensors so the diver (and electronics, if any) "know" how much gas is in the loop and if more O2 needs to be added. As these rebreathers only expell gas during ascent (or malfunction - but always need to be purged during ascent much like a BCD) they waste very little gas and make very few bubbles. These are known as closed-circuit rebreathers, or CCRs.
Of all the rebreathers, those are the most efficient with the breathing gas, but also the most complicated ones to build, and build well. When compared to OC and depending on depth, CCRs can be 40 times as efficient with the gas supply.
But even a SCR can be very gas efficient, up to eight times as much as open circuit ... that makes diving an alu 80 like having over 600 cu.ft. of gas!
The downside is that rebreathers can be quite expensive, and need more attention before, during and after the dive. They also have more ways of failing, on the other hand, there are more options when they do fail.
Hope that clears it up, if you have questions just ask.
Stefan