In DOE v. CHAO, the Fourth Circuit does a nice job of describing this all important appellate concept. In this Black Lung case, the district court the district court awarded claimant attorney fees for work performed on a contempt motion. However, earlier the district court had denied these fees and Doe did not appeal that ruling. Later on, the district court changed mind and did award fees after the appeal to the Fourth Circuit. The Fourth Circuit held that the denial of fees for work performed on the contempt motion became final after it decided the appeal. Because the mandate rule "forecloses litigation of issues decided by the district court but foregone on appeal or otherwise waived," the district court was not free to deviate from the mandate by reconsidering Buck Doe’s claims for attorneys’ fees that it had denied before appeal and that had not been raised by Buck Doe on cross-appeal.
At base, the Fourth Circuit affirmed that the mandate rule prohibits lower courts, with limited exceptions, from considering questions that the mandate of a higher court has laid to rest. "When matters are decided by an appellate court, its rulings, unless reversed by it or a superior court, bind the lower court." In other words, the mandate is more powerful version of what some might all the law of the case doctrine.