Basically it is space that air can be compressed into. If you have a specific volume of air you compress on every compression stroke then x amount of power is your result. However if you increase even more air (oxygen) in the same amount of given space, then more fuel will be delivered and by law, you will have a bigger explosion which creates more power. By downsizing the combustion chamber size, this is in a round-about way a simulation of this effect. You have in reality the same amount of oxygen but in a smaller amount of space, the comustion chamber pressure right before ignition (or at TDC) will actually be greater than before because it is in a tighter space (aka, higher compression). Compression is exactly what the word sounds like it is, the whole process is trying to cram as much air into a given amount of space. It is a little complicated to explain perfectly but if you can picture it in your head, it is just one of those things you get sometimes. There are limitations to how low you can go and too much compression can harm your engine. Basically it depends what you are using the engine for, but I would suggest to not exceed 10:1 final compression because pump gas might not support it.
Hope this helps a bit.