A more thorough explanation:

An instrument of appeal was a document used in English law to appeal a judgment of divorce made by a trial judge of the Probate, Divorce and Admiralty Division to the full panel of the court. It was used until 1881 when appeals were taken to the Court of Appeal instead of the full panel of the Probate, Divorce and Admiralty Division.

For example, if a couple got divorced and one party was unhappy with the decision made by the trial judge, they could file an instrument of appeal to have the case reviewed by the full panel of the court.

This term is important because it shows how the legal system has evolved over time. The use of the instrument of appeal was replaced by a more efficient process, which allowed for quicker resolution of cases.