What is the connection between the dropping of the atom bomb in 1945 and the commencement of the Cold War?
In August of 1945, the United States dropped two atomic weapons on the Empire of Japan. The strategic objective was to end the Second World War by demonstration of brute force, and to avoid the planned invasion of the Japanese home islands which would cost millions of lives. These two bombings marked the first and only wartime use of nuclear weapons in human history, and demonstrated to the world, and Soviet Union, the United States' capability and willingness to use atomic weapons in open conflict.
In 1945, the United States and Soviet Union were allied against the German Third Reich, and Germany was on its heels. Berlin fell to the Allies in the first days of May. Ten years of war for the Soviets, and 5 for the Americans, had helped to turn both countries into manufacturing powerhouses with well-organized and supplied armed forces.
All of the major powers involved in the Second World War had been working separately to develop nuclear weapons. After the fall of Berlin, both the US and the USSR gained access to the German research and personnel involved in the Third Reich's nuclear program, and in the coming years both would use the German resources to expand and develop their nuclear arsenals.
After the surrender of Japan, the US and USSR, splitting influence along two hemispheres, began an arms race that escalated to the point that any act of outright aggression by either party would be met with an overwhelming second strike response, the end result of such an engagement would be the annihilation of the populations and resources of both sides. This mutually-assured-destruction ensured an uneasy peace for the next several decades. the Cold War was fought using clandestine and proxy-war tactics and the mutual deterrence provided by nuclear armament prevented any outright conflict.