Exhaust gasses exit the combustion chamber, expand in the muffler (also called an 'expansion chamber' for obvious reasons) and escape through the exhaust outlet. Usually there's actually two expansion chambers in series. The idea is basically to convert a series of blasts from the motor (loud!) into a steady stream of air at the end of the muffler (much less loud).

Advantage: quiet

Disadvantage: the resulting backpressure costs you some power.

Tuned pipes in a nutshell:

Exhaust gasses exit the combustion chamber, travel down the tuned pipe. As they go, the create a bit of a vacuum at the engine's exhaust outlet, which helps clear the exhaust out of the motor, and even helps draw more air/fuel through the motor and even into the pipe (more on this in a moment). As the blast of exhaust gas hits the end of the pipe, it is reflected back to the exhaust port, where it (hopefully) packs the fresh air/fuel mixture back into the combustion chamber for the next round. The timing of these events (exhaust port opens, intake port opens, exhaust wave reflects, intake port closes, exhaust port closes) is crucial, and varies with engine speed and pipe dimensions - this is why they're called "tuned" pipes.

Advantage: more power
Disadvantages: more fuel consumption, narrow RPM range for good operation, difficult setup until you get it all tuned.

Most tuned pipes actually have expansion chambers at the end, which helps reduce the noise quite a bit. I'm told that "straight" (meaning unmuffled, not necessarily uncurved) tuned pipes are really really loud.

I've read that the volumetric efficiency of a two-stroke motor with a tuned pipe can actually exceed the volume of the combustion chamber, because of the way the pipe draws through some extra fuel/air mix and then packs it in before the exhaust port closes.

Compatibility

Unless you really enjoy fussing with engines, you probably shouldn't buy a tuned pipe for your motor unless you've seen someone use the same pipe on the same kind of motor with good results. If you enjoy tinkering with engines, feel free to disregard this suggestion. Someone has to do the work, might as well be you. :-)

I've had really good luck with the Helimax tuned pipe on an unmodified OS 32sx. In fact, almost everyone I know who has tried this combination has been happy with it.

A friend has had really poor luck with the Muscle Pipe on an unmodified YS 61 ST2. In fact, everyone I know who has tried this combination has had poor luck with it. Something about that motor just doesn't like it. Few people (if any) have been able to get them tuned together.