What is Petty Session?

Legal Definition
A court of petty sessions was a local court consisting of magistrates held for a hundred in England, Wales, and Ireland.

They were also later established in British colonies, including Australia.
-- Wikipedia
Legal Definition
In English law. A special or petty session la sometimes kept in corporations and counties at large by a few justices, for dispatching smaller business in the neighborhood between the times of the general sessions; as for licensing alehouses, passing the accounts of the parish officers, etc.. Brown.
-- Black's Law Dictionary
Legal Definition
A justice's court of summary jurisdiction.
-- Ballentine's Law Dictionary