On appeal from the decision of a lower court or petition for review of the order of an administrative agency, remand refers to an order returning the case to the lower court or agency in order for it to proceed in a manner consistent with the rules and standards enunciated in the appellate court's opinion.

For example, let's say that the lower court in a capital case admitted inappropriate "victim impact" testimony during the guilt phase of the trial. If the defendant gets convicted, on appeal, he'll likely argue that the verdict should be thrown out because admission of that evidence is reversible error. If the appellate court agrees, it will reverse the lower court's decision, and remand the case back to the lower court, so that it can proceed with a new trial in which the improper evidence is not introduced. The standard formula used by appellate courts in this case is:

We remand the case to the court below for proceedings not inconsistent with this opinion.