Short answers, pulled from the story.
The Potsdam Declaration was a formal ultimatum calling for the unconditional surrender of all Japanese armed forces during World War II. It was issued on the 26th of July, 1945, by United States President Harry S. Truman, British Prime Minister Winston Churchill, and Chinese President Chiang Kai-shek. It warned that if Japan refused, it would face prompt and utter destruction.
The declaration required the permanent elimination of Japan's militarist leadership, Allied occupation of designated points in Japanese territory, and the limitation of Japanese sovereignty to the islands of Honshu, Hokkaido, Kyushu, and Shikoku. It also promised that disarmed soldiers could return home, that Japan would retain industries sufficient for its economy, and that Allied forces would withdraw once a responsible government was established.
Foreign Minister Shigenori Tōgō recommended postponing any reply until Japan received a response from the Soviet Union, which Japan hoped would mediate peace negotiations. Prime Minister Kantarō Suzuki then addressed the press using the word mokusatsu, which the United States interpreted as rejection by ignoring. Whether mokusatsu meant outright rejection or simply withholding comment remains historically contested.
The United States Army Air Forces dropped the first atomic bomb on Hiroshima on the 6th of August, 1945, and the second on Nagasaki on the 9th of August, 1945. That same day, the Soviet Union declared war on Japan and invaded Manchuria on three fronts. Emperor Hirohito announced Japan's acceptance of the Potsdam Declaration at 1200 JST on the 15th of August, 1945, and formal surrender documents were signed on the 2nd of September, 1945.
Joseph Stalin declined to endorse the ultimatum at Potsdam because the Soviet Union was not yet at war with Japan at the time of the conference. Stalin committed to subscribing to the declaration upon Soviet entry into the war, which was scheduled for early August. The Soviet Union formally adhered to the Potsdam Declaration on the 8th of August, 1945.
The Potsdam Declaration limited Japanese sovereignty to the four main islands and served as the legal basis for the Allied occupation's reforms, as stipulated in the Japanese Instrument of Surrender after General MacArthur landed in Japan in September 1945. The People's Republic of China cites the declaration as one of the foundations of the One-China Principle, the position that Taiwan is part of China.