For subsequent types of praefectura, see Prefect

Prefect

Prefect is a magisterial title of varying definition....

.

A prefecture (from the Latin

Latin

Latin is an Italic language originally spoken in Latium and Ancient Rome. It, along with most European languages, is a descendant of the ancient Proto-Indo-European language. Although it is considered a dead language, a number of scholars and members of the Christian clergy speak it fluently, and...

 Praefectura) is an administrative jurisdiction or subdivision in any of various countries and within some international church structures, and in antiquity a Roman district governed by an appointed prefect.
Prefecture most commonly refers to a self-governing body or area since the tetrarchy

Tetrarchy

The term Tetrarchy describes any system of government where power is divided among four individuals, but usually refers to the tetrarchy instituted by Roman Emperor Diocletian in 293, marking the end of the Crisis of the Third Century and the recovery of the Roman Empire...

 when Emperor Diocletian

Diocletian

Diocletian |latinized]] upon his accession to Diocletian . c. 22 December 244  – 3 December 311), was a Roman Emperor from 284 to 305....

 divided the Roman Empire

Roman Empire

The Roman Empire was the post-Republican period of the ancient Roman civilization, characterised by an autocratic form of government and large territorial holdings in Europe and around the Mediterranean....

 into four districts (each divided into dioceses

Roman diocese

A Roman or civil diocese was one of the administrative divisions of the later Roman Empire, starting with the Tetrarchy. It formed the intermediate level of government, grouping several provinces and being in turn subordinated to a praetorian prefecture....

, grouped under a Vicarius

Vicarius

Vicarius is a Latin word, meaning substitute or deputy. It is the root and origin of the English word "vicar" and cognate to the Persian word most familiar in the variant vizier....

 (a number of Roman province

Roman province

In Ancient Rome, a province was the basic, and, until the Tetrarchy , largest territorial and administrative unit of the empire's territorial possessions outside of Italy...

s, listed under that article), although he maintained two pretorian prefectures as an administrative level above the also surviving dioceses (a few of which were split).
As canon law

Canon law (Catholic Church)

The canon law of the Catholic Church, is a fully developed legal system, with all the necessary elements: courts, lawyers, judges, a fully articulated legal code and principles of legal interpretation. It lacks the necessary binding force present in most modern day legal systems. The academic...

 is strongly inspired by Roman law, it is not surprising that the Catholic Church has several offices under a prefect.