It's basically a ratio that tells you how much of volume is in the cylinder when the piston is at the bottom of it's stroke compared to when the piston is at the top of it's stroke. The higher the compression ratio the more power you can get out of it, but higher compression is much more vulnerable to knocking.
Take a Coffee can that is 10 centimeters high and has a total volume of 100 cc's. (This woud represent a cylinder)
Put a top on the can, then take a "piston" and push it up from the bottom and stop 9 centimeters up and "compress" the air into that last 1 cm of space.
You have just created a 10:1 compression ratio and crammed 90cc's of air into a 10cc air space.