How does compression increase engine power?

When you increase compression , you increase the potential energy to drive the piston down faster. The air and fuel in the combustion chamber are squeezed to a high pressure(into a smaller space) because the piston top is closer to the cylinder head base. When the mixture of fuel and air are ignited by the spark plug , it burns faster and with more force on the top of the piston.

A higher compression engine, also creates a stonger vacuum signal, when the intake valve is opened, allowing for a more complete filling of the cylinder. It is needed when using a long duration cam/ large port heads and manifold for high rpm power band which cause a drop in the intake vacuum signal.