A court-martial (plural courts-martial, as "martial" is postpositive) is a military court. A court-martial is empowered to determine the guilt of members of the armed forces subject to military law, and, if the defendant is found guilty, to decide upon punishment.
Most militaries maintain a court-martial system to try cases in which a breach of military discipline may have occurred. Some countries, however, have no court-martial in time of peace; this is the case in France and Germany, for example, where ordinary, civilian courts are used instead.
In addition, courts-martial may be used to try prisoners of war for war crimes. The Geneva Convention requires that POWs who are on trial for war crimes be subject to the same procedures as would be the holding army's own soldiers.
Most navies have a standard court-martial which convenes whenever a ship is lost; this does not presume that the captain should be suspected of wrongdoing, but merely that the circumstances surrounding the loss of the ship should be made part of the official record. Many ship captains will actually insist on a court-martial in such circumstances.
Read more about Court-martial: Composition, Jurisdiction