Now what is that compression of a engine you hear so much about?

When you now the basic principle of a internal combustion engine, you will know it has 4 strokes (suck in air, compression of the air, ignition and finally blow out the exhaust gasses). 

So the compression is all about the second stroke the engine makes in it's cycle: Compression of the air.

After the piston moved down to suck the air into the cylinder, it has to come back up again aswell.

During the transition of the down movement into a upwards movement, all the valves (intake and exhaust valves) are shut. And since the cylinder is sealed by means of the pistonrings, the air has nowhere to go.

So it will be compressed by the piston moving up again.

This is basicly the compression stroke.

We need this stroke to turn the oxygen in the air and the fuel that is injected into the combustion chamber into a combustible mixture. To do this, there is a certain ratio bewteen the air and fuel. The ratio should be somewhere around 1:14 (14 parts oxygen for every part of fuel).

When the mixture isn't correct, it will not ignite properly. The engine won't run well or won't run at all.

So in short: No combustion, means not a good mixture, means not a good ignition, means no performance out of the engine.