Why can the US Supreme Court hear cases on appeal from lower courts?

This is called appellate jurisdiction, and is the type of jurisdiction the Supreme Court most often exercises.

A higher court may have appellate jurisdiction to hear a case from a lower court. Additionally, an appeal will not bar a subsequent trial of the same crime if the defendant was not acquitted. Therefore, if a defendant is prosecuted and found guilty, and then successfully appeals the conviction, the government is not barred from retrying the defendant for the crime.

In addition, the Fifth Amendment does not protect a person from being tried by two or more "separate governments." Thus, both the federal government and the state government are able to charge and prosecute one person for the same criminal act, which is often the case with drug related crimes. As well, two or more states can prosecute and try a person for the same criminal act if they have jurisdiction. In some cases, a person can be charged in both federal and state courts; however, in most cases, one or the other will try the defendant.