Kokura was the intended target, but had been obscured by clouds. Major Sweeney had orders to drop the bomb visually and so moved on to Nagasaki, the secondary target. Since their fuel was getting low and Sweeney didn't wan't to dump the bomb in the East China Sea, he decided to make a radar bombing run. However, enough of a opening came in the cloud cover to allow the bombardier to confirm Nagasaki, and the bomb was dropped with ground zero being about 3/4 mile from the planned target. This resulted in lower overall casualties than would have been otherwise, as most of the blast was confined in the Urakami valley.
The more-often recognized B-29 "Enola Gay" preceded Bockscar in dropping a nuclear weapon on Japan. In the language of warfare, the leveling of Nagasaki after the Hiroshima decimation demonstrated the US Armed Forces' willingness and ability to repeat this type of crippling aerial attack.
Many consider that the bombings mounted by this pair of B-29s provided the greatest impetus behind the subsequent Japanese surrender, thus bringing to an end the fighting of World War II.
This historic aircraft is sometimes referred to as "Bocks Car" or "Bock's Car" but the actual name painted on the aircraft was "Bockscar".