A more thorough explanation:

The Duchy Court of Lancaster was a court in English law that had special equity jurisdiction. It was similar to the equity courts of chancery. The court was presided over by the chancellor or deputy of the Duchy of Lancaster. The court dealt with issues primarily relating to land held by the Crown in right of the Duchy.

One example of a case that would be heard in the Duchy Court of Lancaster is a dispute over the ownership of land that is held by the Crown in right of the Duchy. Another example is a case involving the use of land that is owned by the Duchy of Lancaster.

These examples illustrate the definition of the Duchy Court of Lancaster because they show that the court had jurisdiction over issues related to land owned by the Crown in right of the Duchy. The court was responsible for resolving disputes and making decisions about the use of this land.