What is the origin of the idiom "at Her Majesty's pleasure" and when to use it?

The idiom "at Her Majesty's pleasure" has its origins in British law and is associated with the legal system of the United Kingdom. It has been used for centuries and is rooted in the authority of the British monarch. The concept of royal prerogative, including the power to determine the length of imprisonment, has historical roots in the discretionary powers of the British crown. It is used when referring to individuals, often juveniles or those deemed mentally unfit, who are sentenced without a fixed term and are subject to the discretion of the monarch or relevant authorities for determining the duration of their confinement.