compression ratio is the ability of the engine to compress air.
For example, a 1.6 litres (rounded number, actual is around 159x)
So a 4 piston 1.6 engine has roughly 400cc per cylinder. Not exact number, combustion chamber volume affects this number as well, which is why you see manufacturers ending up with 1598, 1585ccs instead of a full 1600cc, since combustion chamber designs actually alter the cc of the engine (not much, but still that little bit counts!)
At BDC (the piston is at the bottomost position), let's say that it has sucked in 400cc's of air.
At TDC (the piston is at the topmost position), let's say it compressed that 400cc's of air into the space of 40cc, thus it has a 10.0 compression ratio.
Static compression assumes that the valves are shut completely during compression stroke (engine have 4 strokes, one of them is the compression stroke)
In real life, valves do not close immediately like magic, they take time to close (much faster than you can blink your eye! but they do not close instantly if you know what I mean).
Depending on cam setup, the valves will close later in the compression stage to help engine breathing at high rpms (that's why race cams or cams that are set with higher overlap idle badly).
As such, the real life compression ratio (or known as dynamic compression ratio) will vary highly with static compression ratio.
Or.... (this came to mind after I typed the above, Damn! I should have thought of this sooner!)
Static compression ratio is calculated via the (stroke x bore) ( +piston dish or -piston dome volume) + combustion chamber volume / combustion chamber volume ( +piston dish or -piston dome volume).
Dynamic compression ratio is measured with a compression tester, and cannot be calculated, unless you're a rocket scientist that thinks math is fun.
Higher compression results in more power since the air+fuel is compressed more, much like how turbo gets it's power by stuffing more air into each cyclinder regardless of it's capacity. Almost same, but dissimilar.
Hope that helps.. I wondered myself last year, and took up researching the topic.
p.s.
Oh, why bother with static compression then? (A question I posed when I found out the above!)It just gives you a rough idea how much compression to expect when building your engine. Although inaccurate, a 13.x static compression ratio will not work with regular fuel, no matter what you do (unless you retard the ignition timing like mad, like what my friend does with his B20B with 12.8 dynamic compression ratio, an inefficent solution, but with a spare tank of racing fuel.. watch out!)