G0 ; G1 ; G2 ???

 From:  Schbeurd

Following the world famous "spiral thread" (LOL), I think it's time to start another topic where the "technical minded" guys will explain in (very) simple words what is that G0; G1; G2 curvature (?) you sometimes refer to. ;-)
As the terms appear in some discussions and also in the application (the blend tool being an example), an explanation of what it is would be welcome. You know, something easy to understand for a complete beginner or someone coming from poly modeling software. I must say that I'm a bit clueless...