President Harry Truman, by August 1945, had to take an important decision about ending the war with Japan as soon as possible, knowing that they (Japanese) already lost the war at that moment. President Truman had four options: 1. Continue conventional bombing; 2. A ground invasion of Japan; 3. Demonstration of the bomb on a deserted island; or, 4. Use of the bomb on a populated Japanese city. After careful considerations, President Truman, his advisors, and commanders decided to bomb Hiroshima to make a strong impression on Japanese Emperor, Army, and civilians.
If dropping the bomb was the right decision or not, it's still not easy to affirm. However, the goal was to get a quick surrender from Japan and to do not extend the war uselessly. In that sense, it was a painful and effective decision.