Discretionary jurisdiction is a legal term used to describe a circumstance where a court has the power to decide whether to hear a particular case brought before it. Most courts have no such power, and must entertain any case properly filed, so long as the court has subject matter jurisdiction over the questions of law which must be decided, and in personam jurisdiction over the parties to the case.
Typically, the highest court in a state or country will have discretionary jurisdiction. For example, the United States Supreme Court hears cases by a writ of certiorari, essentially meaning that it calls appellants up to the court only if their case is important enough to merit the resources of the court. The Supreme Court employs a 'rule of four', meaning that four justices have to think the case is important enough to hear before the court will grant it review. Many state supreme courts use a similar process to choose which cases they will hear.