What does it mean for a higher court to uphold a lower courts decision?

Answer 1

That means a case heard in a trial court was appealed to an appellate court; the appellate court agreed with the lower court's decision, and determined the case was conducted properly. When this happens, the appellate court "affirms" the trial court decision, and that decision becomes final unless the case is carried to a higher appellate court that reverses the trial court's decision.

Answer 2

A "higher court" is typically acting in an appellate capacity. The "lower court" is often the trial court. The trial court is charged with hearing evidence, making rulings on the admissibility of evidence, and applying the correct law to the facts. From that, a decision is reached on the merits of the case.

When an appellate (higher) court upholds the lower court's decision, it essentially means that it believes that the trial court applied the correct law and applied it correctly.

Answer 3

We call this "Certiorari". It's the ability for the higher courts to review, amend, and direct the lower courts to take a specific action requiring a case submitted to them. Typically, laymens call it an appeal.