Here's an image
#1 Is the flywheel. That bolts up to the engine crankshaft. Its a bit hunk of metal that holds rotational momentum and makes it easy for take offs etc.
It bolts up to the pressure plate, which is #8, and between them is the clutch plate, #9.
The outside part of #9 is the clutch lining. Thats the bit that has the diagonal lines on it. The pressure plate has a surface that makes contact with the clutch lining and clamps it against the flywheel.
The center of the clutch plate is connected to the input shaft of the gearbox, and thats how the power from the engine gets in.
When you push your foot on the clutch, a fork pushes the release bearing (#7) on to those forks you can see in the center of the pressure plate (Thats #8 remember) which it turn pulls off the surface that makes contact with the clutch plate lining.
This means the flywheel and pressure plate (which are bolted to the engine) are no longer in contact with the clutch plate (which is connected to the gearbox), so its disengaged, and you can change gears.
Motorsport is like sex. You could take it to track and have a long, enjoyable session, or you could take it to the strip and get it over with in less than 20 seconds.