A more thorough explanation:

Definition: A convening authority is a military officer, usually a commanding officer, who has the power to convene or has convened a court-martial.

Example: Captain Smith is the convening authority for the court-martial of Private Johnson.

Explanation: In this example, Captain Smith has the power to convene the court-martial of Private Johnson. As the convening authority, Captain Smith has the responsibility to ensure that the court-martial is conducted fairly and impartially.