That's it in a nutshell, really. There are many types of engines that do not have cylinders, of which you are likely to encounter ZERO- unless you're in the habit of playing with jets, turbines, rockets, the aforementioned Wankel-type rotaries.... The internal combustion engines powering cars, trucks, lawnmowers, whatever (including diesels) have pistons in cylinders.
To clarify the displacement thing a wee bit: The engine's piston travels up and down in the cylinder. It is the volume of that cylinder (or the combined volume of multiple cylinders) that equate to the displacement. This is most commonly measured in cubic centimetres (cc's), or in the old Imperial way, CID (Cubic Inches Displacement). the 50cc's literally equates to the effective volume of the cylinder engine in such a size.
I want to know more about your local regulations. I have heard of such licensing regarding mopeds and scooters, but I have NEVER heard of these regulations pertaining to go karts. Where are you from, and can you point me to where you found these laws?
For further engine theory, you need to read up on four-cycle and two-cycle internal combustion engine theory- this is basic stuff and should be understood by anyone who so much as operates an engine.
EDIT- Please note that a Cubic Centimetre is exactly equal to a millilitre (ml). A 1-litre engine, for example also equals 1000cc or 1000ml. The effective cylinder volume literally would hold a litre of water...
