A more thorough explanation:

The Court of General Quarter Sessions of the Peace was a court of criminal jurisdiction held in each county (or borough) once every quarter of a year. It was made up of a county's justices of the peace and had the power to try and determine all felonies and trespasses. The court committed certain cases to the Assizes. Quarter Sessions were abolished in 1971, with most jurisdiction transferred to the Crown Court.

For example, in England, the Court of General Quarter Sessions of the Peace was held before two or more justices of the peace, one of which must be of the quorum. The court's jurisdiction extended to trying and determining all felonies and trespasses, although they seldom tried any greater offense than small felonies within the benefit of clergy.

In some states in the US, the Court of Quarter Sessions of the Peace was held four times a year and had jurisdiction over misdemeanors and occasionally tasks of an administrative nature, such as the care of public roads and bridges.

These examples illustrate how the Court of General Quarter Sessions of the Peace was a court of criminal jurisdiction that had the power to try and determine certain cases. It was made up of justices of the peace and was held at regular intervals in each county or borough.