From 1361 there have been laws which established justices of the peace to conduct courts in each county.
From 1388 the justices in each county were required to meeet four times a year, hence the quarter sessions. Not only were they responsible for keeping the law and handing out sentences to criminals, by the 18th century they were also responsible for the upkeep of bridges and highways and for determinining prices and wages and the administration of the poor law. It was only after 1888 when the new councils were formed that a lot of these duties passed to the councils and left the JP's as law officers. Quarter Sessions finally dissapeared in 1971.
Quarter Session Rolls exist for Cumbria from the 17th Century in some cases. The old Lancashire area records are probably the oldest. If your ancestors had transgressed the law you may find them in the Rolls, but you may also find them in electoral registers, land tax returns, militia lists, poll books and all the other records of the time. Cumberland records are in Carlisle, Westmorland in Kendal, the Furness area of Lancashire in Preston and the Sedbergh area are in Wakefield.