Chu Chu,
Under high compression you can burn more fuel in a given amount of time as high compression crams in more oxygen molecules et al and you simply release more energy per unit time from the increased levels of combustion.
Specifically you release enough extra energy available to do useful work than you need to use in the compression step. The relationship between compression and power out is exponential and not linear. I will play hunt the graphs.
turbo graphs - Google Search
Increased expansion comes from now having generated more combustion product molecules CO2/H2O/NOx and friends in a given space or volume (can/cylinder etc.)
Gas turbine and piston engines are both fully open systems thermodynamically, exchanging energy and matter with their surroundings.
CW