The quote indicates Cromwell's predisposition to have Charles I beheaded for treason and, at the same time, bring an end to the monarchy. His intention was not only to dispose of Charles but also to dispose of the monarchy altogether.
Charles I and the English Parliament had experienced a long and bitter disagreement; primarily because of Charles's attempt to rule absolutely without incorporating Parliament's representation. However, Charles could not raise taxes without the consent of Parliament and was forced to reopen it. In 1641, Parliament passed the Grand Remonstrance calling for reforms and complained that Charles had attempted to subvert English law. The English Civil War resulted, which was more a war of words with over 2,000 pamphlets issued than an actual war of weapons. Charles's forces were ultimately defeated and he attempted to surrender to the Scots, with whom England was also at war; but they delivered him to Parliament by which he was held prisoner. Cromwell had Parliament pass a motion that no further addresses to the King would be made. To Cromwell, the monarchy had effectively come to an end even while Charles was still alive.
The so called "Rump Parliament," which consisted of only one fifth the normal number of members, appointed a high court to try Charles. Charles refused to defend himself, and was condemned; he was executed by beheading on January 30, 1649.