Two strokes are all about the exhaust. When combustion occurs in a two stroke, the piston is pushed down by the expanding gases uncovering the exhaust port. The exhaust gas rushes out into the header pipe and a pressure wave is created. This wave can be either positive or negative in pressure. If it is a positive wave and hits a change in diameter in the tubing of the exhaust pipe it changes to a negative wave. Hit another change in diameter and the wave changes back to positive. This wave pressure can be as high as seven pounds per square inch (Both positive and negative waves) and travels at 1600 to 1700 feet per second.
If the pipe is made just right, a wave with negative pressure reaches the exhaust port just as it is fully open. This sucks the exhaust AND part of the new intake charge into the exhaust pipe. Then, just before the piston closes the exhaust port, this negative wave changes to a positive wave and pushes the fresh intake fuel charge BACK into the cylinder. All this happens in three to four thousands of a second. This sort of supercharges the engine, giving the high power out put of a two stroke engine. Without that properly designed exhaust pipe called an "Expansion Chamber", the two stroke engine will have no real power!
There is only one draw back to all this and that is that this supercharging only happens at the specific RPM that the pipe was designed for. Running the engine at any RPM above or below the designed RPM and the supercharging effect will be much less effective. That is why two strokes have such a narrow power band.
Here is a really nice Gif animation showing how it all works. I got this from a web site, made by Joseph A. Schuster in 1997. I have tried to e-mail him but there was no response. The site is no longer online. I am assuming he would want you to have this. (523Kb)
One problem with two stroke exhausts is that they can get plugged up with carbon from the oil used to lubricate the engine. The bike will start easily but just will not rev up. This is especially true of quite exhausts. If the exhaust has removable baffles or is fiberglass packed, you can easily clean them and replace the fiberglass packing. If the baffles are not removable it is much harder to clean them. Many stock two stroke exhausts have non removable baffles or have only one or two baffles that are removable. The different baffles collect the unburned carbon and plug up but you can't easily get to them. There are several cures. Non of which are easy or cheap.