Cromwell's rule would be remembered for his strict enforcement of a broad doctrine of public morality, through Major-Generals in each province of his protectorate. Their job was to make England a little more godly, many were Puritans like Cromwell and cracked down on deviant behaviour - such as plays, dancing and drinking. There were also attempts at banning Christmas.
Naturally, the military rule of the Cromwell era became synonymous with Puritanism and when Oliver died in 1658, his son Richard succeeded as Lord Protector, yet was not as authoritative as his father, lacking any power in the Parliament or any support in the military. His stint in charge became famous for corruption and anarchy and for many of the people who were viciously taxed or morally policed during the Cromwell era, monarchy represented stability. As such, when Charles II eventually returned to London, he was received with great popular support.
When Richard Cromwell resigned, Parliament was dissolved and many members began to collect political power, only to be promptly dismissed by General Lambert again, after a dispute between Parliament and the Army. Lambert proposed to set up military rule. This did not impress one of Cromwell's most loyal assistants, General Monck, who rushed from Scotland to London and collected together the MPs of the dissolved parliament. The MPs demanded that the monarchy was restored and fresh elections were held.
This newly elected Parliament - 'The Convention Parliament' - negotiated with Charles, who accepted their conditions as outlined in the Declaration of Breda (and amendments to it in Parliament). The main provisions of the declaration were that:
The Convention Parliament agreed to the conditions set out at Breda, and invited Charles II to ascend, becoming King of England on May 29, 1660.