No quarter

refusal to show mercy to the defeated, especially by slaughtering prisoners of war

In an armed conflict, the loser has the possibility to surrender to the winner (or to give up). This usually means that the person will be made a prisoner of war, and that there will be a trial, to determine whether the person is guilty of one of the crimes of war. There's also the promise, that the person who surrenders will be left alive. Certain parts of the military were known for not allowing ennemy fighters to surrender; this was known as no quarter. The Hague Convention of 1899 made this practice illegal, and a war crime. Since then, the practice has become part of customary international law. This means it is also binding for parties who did not sign the Hague Convention.