A more thorough explanation:

Definition: In military law, a supervisory authority is an officer who has the power to review trial records of summary and special court-martial cases after the convening authority has reviewed them. This officer exercises general court-martial jurisdiction.

Example: Let's say a soldier is accused of violating military law and is tried in a special court-martial. The convening authority, who is usually the commanding officer, reviews the trial records and makes a decision. However, if the soldier is not satisfied with the decision, they can request a review by the supervisory authority. This officer will then review the trial records and make a final decision.

Explanation: The example illustrates how a supervisory authority has the power to review trial records and make a final decision in military court cases. This officer acts as a check and balance to ensure that the convening authority's decision is fair and just. The supervisory authority has the power to uphold, modify, or reverse the decision made by the convening authority.