compression ratio is just the ratio of air at the bottom of the stroke vs top of the stroke
say that you have a motor with a 1000cc cylinder volume and a 100cc head volume. when it compresses all of that air its in a 100cc volume.
so that would be 1000:100 or 10:1

higher compression ratios are more thermally efficient to a point.
for each point in compression you go up, you gain 3% efficiency.

High compression turbo motors have better off boost efficiency as well as faster spool and better transient response. since turbos make power by extracting thermal enery from the exhaust gasses. you basically have more power at a given boost level vs a lower compression motor (provided tuning)

we've built 13:1 Integra type-r motors that have made 350whp on pump gas with a gt28rs, it had increadble response (almost 0 lag) and ran forever.

our motors are fine to boost, the only weak link would be the headgaskets and head bolts, i think our gaskets are fiber based, but ive never seen one. MLS would be preferred.

Ringland thickness and position also are a factor. Motors designed for boost have a thicker upper ring land and they place the top ring further down on the piston to move it away from hot combustion gasses.