What is Cancellation of Removal in immigration court?

I would appreciate if you can tell me who initiates this in immigration court? Is it the judge who says you qualify or not or it is the LPR who decides whether he or she qualifies and then requests the judge to get him the cancellation during the hearing? How does this specific process work. When someone has been denied the waiver and has been sent to immigration court to renew the green card through the judge, is the cancellation of removal the only way to get the green card assuming that the LPR qualifies to one of the option of the removals available? What if the LPR has been present in the US for only 3 years, does it mean that he or she will be better off convincing the judge through evidences of bonafides instead, seeing that he/she does not qualify for any cancellation of removals?