Starting with the moment the engine fires, forcing the piston down and the exhaust port begins to open. At this point the cycle starts. The exhaust gases are forced out of the engine and start to travel down the 'header' section of the pipe. Before long the gas reaches the expanding / divergent / front (the names vary) cone. The effect is a pressure drop, creating a vacuum which helps 'pull' the remaining exhaust gases out of the engine.
Not only are the exhaust gases being 'sucked' out of the engine, the fresh intake mixture is being 'drawn' into the combustion chamber from the crankcase via the transfer port. Some of this new charge will follow the exhaust gas straight through the still open exhaust port.
The exhaust gas travels down the pipe, through the expanding cone till it meets the rear reflecting / converging cone. The converging cone forces the pressure to rise, generating a pressure wave which reflects back towards the exhaust port.

As the reflected wave approaches the exhaust port, it forces the fresh mixture (which flowed through the combustion chamber), back into the combustion chamber. As the transfer port closes before the exhaust port this results in a pressurised charge in the combustion chamber as the exhaust port closes, - the result - more power. See diagram below.