What cases are heard in the supreme court?

The Supreme Court decides cases that are appealed by a lower court; a lower court has made a decision and one of the parties feels strongly enough that the decision was wrong that they make an appeal to the Supreme Court. The Supreme Court reviews the cases and determines which ones they will hear, they have the ability to decline to review a case.

The Supreme Court doesn't hear only appeals, there are situations where it is the court of original jurisdiction. In situations where there is a disagreement between states, the Supreme Court has the authority to decide.