To abdicate is to?

abdicate is another word for stepping down , an example is to step down as a prime minister or a king.

one of the most famous abdication is that of King Edward VIII of the United Kingdom in 1936. Edward abdicated the British throne in order to marry American divorcee Wallis Simpson, over the objections of the British establishment, the governments of the Commonwealth, the royal family and the Church of England. (See Abdication Crisis of Edward VIII.) This was also the first time in history that the British crown was surrendered entirely voluntarily. Richard II of England, for example, was forced to abdicate after power was seized by his cousin, Henry Bolingbroke, while Richard was out of the country.
During the Glorious Revolution in 1688, James II of England and VII of Scotland fled to France, dropping the Great Seal of the Realm into the Thames, and the question was discussed in Parliament whether he had forfeited the throne or had abdicated. The latter designation was agreed upon, for, in a full assembly of the Lords and Commons, it was resolved in spite of James's protest "that King James II having endeavoured to subvert the constitution of the kingdom, by breaking the original contract between king and people, and, by the advice of Jesuits and other wicked persons, having violated the fundamental laws, and having withdrawn himself out of this kingdom, has abdicated the government, and that the throne is thereby vacant." The Scottish parliament pronounced a decree of forfeiture and deposition.
Because the title to the Crown depends upon statute, particularly the Act of Settlement 1701, a Royal Abdication can only be effected by an Act of Parliament; under the terms of the Statute of Westminster 1931, such an act must be passed by the parliament of all sixteen Commonwealth realms. To give legal effect to the abdication of King Edward VIII, His Majesty's Declaration of Abdication Act 1936 was passed.

(information from Wikipedia)