When you combust the mixture you create an exhaust gas that is less dense, so it wants to occupy a larger volume. Until you open the exhaust valve, the only option for the gas is to push the piston down. When you open the exhaust valve up, the exhaust gas in the cylinder is still at a higher pressure than STP, so it pushes itself out through the (now open) exhaust port and into the exhaust manifold or header primary and then subsequent exhaust pulses from that cylinder and the others help to push old exhaust gasses out the entire system.

When something is under a lot of pressure, you can fit it through a smaller hole faster you could fit it through a larger hole at low pressure.

 

You'll have been beating up on Eric pretty good.
So I guess i'm going to have to jump in here and agree with him on one point.
The Gross volume of the cyclinder does not change. Only the net volume between the top and bottom of the stroke. i.e. the volume of the cyclinder at the bottom of the intake stroke is exactly the same as the volume at the bottom of the combustion stroke, only the pressure is different.
And no I'm not considering valve over lap and duration and all that crap!

Cheers!!!