How are the manhattan project and the end of the war related? where does this all culminate?

The Manhattan project was the project behind the American atomic bomb. Nearing the end of WWII, President Rosevelt died and Truman took over the Presidency. Truman then learned of the U.S. plan to have an atomic bomb. In the end, Truman decided to use this power (the atomic bomb) that was created by means of the Manhattan Project, and bomb Nagasaki and Hiroshima, powerfully stopping the fighting between the US and Japan in the Pacific Theatre in WWII.

The Manhattan project was a huge top secret development that even the Vice President didn't know of. During the project, little boy and big man, the atomic bombs dropped on Hiroshima and Nagasaki were created. So, since dropping the atomic bombs caused the Japanese to surrender and them being created during the Manhattan project makes them related. 

Idon’t understand a word going on right now lol