A more thorough explanation:

Definition: Magisterial means relating to the character, office, powers, or duties of a magistrate.

Examples:

• The judge's magisterial tone commanded respect in the courtroom.
• The mayor's magisterial authority allowed him to make important decisions for the city.

These examples illustrate how magisterial is used to describe someone or something that has the power and authority of a magistrate. In the first example, the judge's magisterial tone shows that he has the authority to make decisions in the courtroom. In the second example, the mayor's magisterial authority allows him to make important decisions for the city.