A more thorough explanation:

The Court of Private Land Claims was a federal court that existed from 1891 to 1895. It had the power to hear claims made by private parties regarding public-domain land located in the southwestern part of the United States. These claims were based on Spanish or Mexican grants.

For example, if a person believed that they had a legal right to a piece of land that was originally granted by the Spanish government, they could bring their claim to the Court of Private Land Claims. The court would then review the evidence and make a decision about who had the legal right to the land.

Another example would be if a group of people believed that they had a legal right to a large area of land that had been granted by the Mexican government. They could bring their claim to the Court of Private Land Claims, and the court would decide whether or not their claim was valid.

These examples illustrate how the Court of Private Land Claims had the power to settle disputes over land ownership in the southwestern United States.