I've been meaning to write this for a while now. This question gets asked all the time and there's not really a thread about it yet. I'm going to give you guys a brief history of how it got started and go over the ins and outs of what they can do for you.
Roughly about the time I got serious about the hobby, a few people realized that there was an alternative to the hobby regulators on the market at that time. The JBJ, the Milwaukee, the Azoo, ect... They all had reliability/quality issues. They all seemed to suffer from needle valves that would 'float', pressure issues as the cylinder ran out, well... you get the idea. If you had the money, you could order from gla, aquariumplants.com, Rex Grigg, or Sumo. These were a lot better in terms of quality but you were going to pay a premium for better equipment.
Enter [that auction site I can't type here]. Some of us quickly figured out that people where selling 2-stage, industrial, lab grade, high purity regulators for cheap. Before demand drove the price up, we were paying very little for a regulator that might retail in the 500-1000 dollar range. Obviously these regulators where way more dependable than the ones we're all familiar with. You could find deals on all the other components that make up the assembly too. After it was all said and done, you'd have a unit that would spank any commercially available regulator in the hobby for 100-150 dollar range. That's were it started.
Not long after, people started increasing the 'bling' factor. Folks started threads showing us how they did it, what parts they used. People started playing around with different metering(needle) valves and solenoids. All of a sudden, this became a hobby within a hobby for some of us. Ultimately, we started rolling out solid stainless steel regulators that if you bought retail would cost more than a used car.
Ok... so now that we know how it happened, I'll explain what it is and why it's a good idea.
A regulator's job is to lower cylinder pressure to a level that is in a usable range for whatever you're going to use a gas for. For us, we're dropping pressure to a low, consistent level to get it into our water column. The problem with some gasses, like CO2, is that when the cylinder starts to run out, the regulator can have a difficult time keeping the pressure consistent. Normally, it's just a few psi on a single stage regulator. Every once in a while,it's more than that and that's what can result in disaster in your aquarium. It's pretty rare though.
This is one of the things that popularized the 2-stage regulator. It's purpose in life is to provide consistent psi no matter how the pressure in the cylinder changes. It does this by basically stacking two regulators in one body. This is where the term dual stage or 2-stage comes from. The first stage drops the pressure to a fixed point where the second stage can handle it in a consistent way. The second stage is the part we can adjust to the psi we want to use.
You shouldn't consider one just because you're afraid of or just want to eliminate the possibility of the dreaded 'end of tank dump'. It just doesn't happen often enoungh to justify the expense if money is a concern for you. I don't know, I guess if your disposable income is that great, go for it. What you're really buying is quality and reliability. Some people just like diy projects. They're fun for me. I like hunting for deals and learning new things. So there's that aspect too.
For more info on a basic setup and a really good explain of pressurized co2, please see this thread:
Hope this clears up any questions. If I didn't touch on anything anyone wants to know about, please ask. I'm sure I've overlooked something.