The atomic bombing of Hiroshima and Nagasaki was the time when, on two separate days in August of 1945, the United States dropped one atomic bomb each on these two Japanese cities. These two bombings were the only time in history that atomic/nuclear weapons were ever used by one country against another. The bombings helped to hasten the end of World War II.
By August of 1945, the United States had conquered all important Japanese possessions outside of the home islands. The country then had to face the idea of invading Japan itself. It was clear that this would be an exceedingly bloody operation. The Japanese had fought practically to the last man on islands such as Saipan, Iwo Jima, and Okinawa. In the process, they inflicted heavy casualties on the Americans. American leaders feared a much worse bloodbath if they invaded the home islands.
It was for this reason that the US decided to use the newly-developed atomic bombs on Japan. It was hoped that the bombs would so shock the Japanese that they would agree to surrender, which was something that they had not been willing to do before. This worked in that 6 days after the bombing of Nagasaki, Japan surrendered.
After Germany surrendered in 1945, ending World War II in Europe, the Allies, including the U.S., France, England and the Soviet Union, demanded Japan's unconditional surrender. The Japanese refused, meaning the Allies would have to invade the Japanese mainland, ensuring a bloody and expensive campaign to take the territory step by step.
In the meantime, by the end of July, 1945, the U.S. had finished work on two atomic bombs, one uranium based and one plutonium based. When the Japanese refused to surrender, President Truman authorized the use of these bombs. On August 6, the first atomic bomb was dropped on Hiroshima, destroying the city and killing about 100,000, half on the first day. On August 9, when the Japanese had still not surrendered, the U.S. dropped a second bomb, this one plutonium based, on the city of Nagasaki. This led to between 39,000-80,000 deaths. While the U.S. had already done multiple fire bombings of Japanese cities, killing many, many civilians, the scale and immediacy of the atom bomb destruction was stunning and unprecedented. After the devastation of Nagasaki, the Japanese realized they were outmatched, and signed an unconditional surrender.
At the time, the U.S. justified the bombings as saving the U.S. and its allies from high casualty rates in a ground invasion of Japan, but in the intervening years, the morality of the decision to drop bombs of such destructive magnitude on areas with civilian populations has been strongly questioned.