A more thorough explanation:

Definition: A court of conscience was a local court in England that had jurisdiction over small-debt cases. It was called a court of conscience because its judgments were supposed to be fair and just.

For example, if someone owed money to another person but could not pay it back, the court of conscience would hear the case and make a decision based on what was fair and just for both parties.

County courts took over the jurisdiction of the courts of conscience in 1846.