Read the excellent article on dynamic compression and all in the honda-swap.com articles section.
Massively oversimplified:
if (Boost * compression) < (octane * magic) motor runs
if (Boost * compression) > (octane * magic) motor detonates
More compression almost always means the more power at a given amount of airflow (boost). There is a lot of fine print on this one, however, since higher compression normally requires more ignition retard in order to prevent detonation, which in turn robs power. Most piston/valve/HEAD designs have a point of diminishing returns where increasing compression necessitates ignition retard to the point where power gains are significantly offset. What this means basically is that you want to run as much compression as you can get away with without needing excessive amounts of timing retard, based on the octane and motor design parameters.