If someone is a magistrate — a judge or other civil officer — her position or office is a magistracy. A magistracy in an English town deals with small, local crimes and offenses.
The United States doesn't have magistrates or magistracies, but in many countries they are part of the legal systems. In the UK and Australia, for example, a magistracy hears the majority of cases, with more serious criminal cases being heard by judges in larger courts. Both magistrate and magistracy come from a Latin word, magistratus, "public functionary or civil officer," which shares its root with the English word master.