VJ Day marks the end of WWII, and the cessation of fighting against Japan. It is called "Victory In Japan Day or "Victory Over Japan Day".
The confusion over three dates:
There is some confusion over what date is V-J Day. You can consider any (or all) of three dates as V-J Day. President Harry S. Truman caused some of this confusion........
On August 14, 1945, Japanese Emperor Hirohito cabled the U.S. to surrender, and agreed to the terms of the Potsdam Declaration.
On August 15, 1945, news of the surrender was announced to the world. World War II was finally over. Hostilities ended.
On September 2, 1945, the Japanese formally surrendered aboard the U.S. battleship USS Missouri in Tokyo Bay. President Truman declared this to be V-J Day.
The battleship USS Missouri was chosen for the formal surrender ceremony, as she was named after President Truman's home state.
Regardless of which day you view as VJ Day, World War II was finally over.
(I went with the earliest date so you can choose when to celebrate)