A special or exclusive right, power, or privilege that sets one apart from others.
Example:
It is the prerogative of governors and presidents to grant reprieves and pardons.
In some meetings in ancient Rome, the person asked to vote first on an issue was called the praerogativus. Voting first was considered a privilege, and so the Romans also had the word praerogativa, meaning "preference" or "privilege," from which we get our word prerogative, meaning a special right that one has because of one's office, rank, or character. So a company's president may have the prerogative to occupy the largest office with the best view. In a less official sense, a successful writer may claim the prerogative to invent new words. Speaking frankly is sometimes thought to be the prerogative of the senior citizen, but is probably best exercised with caution.