A petty sessional division was, in England and Wales, the area that a magistrates' court had jurisdiction over. Petty sessional divisions were gradually consolidated in the 20th century (being reorganised in 1953 under the Justices of the Peace Act 1949), and were replaced by local justice areas in 2005.
Petty sessional divisions were established under an Act of 1828 (9 Geo. IV c.43), which formalised the often previously informal summary trials presided over by magistrates. The divisions come from the terminology of the magistrates sitting in petty sessions, as opposed to quarter sessions.
The areas were restated by the Local Government (Petty Sessional Divisions etc.) Order 1973 (SI 1973/1593).
References
Petty sessional division Wikipedia(Text) CC BY-SA