Short answers, pulled from the story.
The Commissar Order, officially titled the Guidelines for the Treatment of Political Commissars, was issued by the German High Command on the 6th of June 1941. It required that any Soviet political commissar captured by German forces be executed immediately, with no legal process, trial, or prisoner-of-war protections. Hitler had laid the ideological groundwork for the order in a series of addresses to senior officers in early 1941.
German historian Jurgen Forster established in 1989 that the Commissar Order was widely enforced, contradicting post-war claims by German Army commanders. The majority of German units carried out the order, and its enforcement led to thousands of executions.
Erich von Manstein passed the Commissar Order to his subordinates, who executed every captured commissar under their control. A British court convicted him of this in 1949. After the war, Manstein falsely claimed he had opposed the order and never enforced it.
Hitler claimed the Hague Conventions of 1899 and 1907 did not apply because the Soviet Union had not signed them. The argument was legally unfounded. Germany had signed the Geneva Convention of 1929, and Article 82 of that convention stated that its provisions remained binding on belligerents who were parties to it, regardless of whether the opposing side had signed.
Hitler cancelled the Commissar Order on the 6th of May 1942, one year after General Eugen Muller had drafted its first written version. The cancellation was prompted by an unintended effect: when Red Army soldiers learned that capture meant execution, they fought harder rather than surrender. Claus von Stauffenberg was among those who cited this consequence in appeals to Hitler.
The Commissar Order was entered as evidence at the Nuremberg trials. It was central to the broader question of whether German generals were legally obligated to follow Hitler's orders even when they knew those orders to be illegal.