What is meant by the eighth amendment’s guarantee that punishments should not be “cruel and unusual”?

Because King George III punished colonists who committed crimes with "hanging" and "tar and feathering," once colonists had come to America, they wanted to change the punishment system. So when they came up with new laws, no cruel and unusual punishments was agreed on. That means that if you commit a crime and are found guilty, they cannot hang you, electrify you, beat you with whips and harsh weapons or tools, etc., as a form of punishment.

United states v.  nixon, 418  u.s.  683 (1974),  was  a landmark  united states supreme court case  that resulted in a unanimous  decision  against president richard  nixon, ordering him to deliver tape recordings  and  other subpoenaed materials to a  federal  district  court.