This was recently asked and answered. The short answer is, the "official" account given after the fact by the people in charge of the bombings was that they thought two bombs would show the Japanese that the US had as many bombs as it could desire. But there are considerable historical factors that complicate this — there isn't a lot of evidence that there was a deliberate, conscious strategy regarding the use of two bombs, other than the fact that they happened (by total coincidence) to have two ready at about the same time. There was initially supposed to be greater time between the bombs but the schedules were modified to fit the weather forecasts. It is not clear that Truman knew that two bombs were going to be dropped in such short succession, either.

Hiya, can you elaborate a bit about what you want to know here, e.g. are you asking: Why did the US drop any atomic bombs at all? Why drop a second bomb, after having dropped the first? Why did they stop at two? Having a bit more clarity on the question will help any of the experts provide a more targeted and complete answer. Thanks!

Because one bomb wasn't enough to force the Imperial Japanese government to surrender immediately.

Yes, the Hiroshima bomb was catastrophic, but the Hiroshima bombing did less immediate damage - not counting fallout and its effects - than the fire-bombing of Tokyo. We view Hiroshima as a watershed now, because it ushered in the Atomic Age, but it was at the time not the worst punch the Japanese had taken all war. Nagasaki showed that the US could destroy cities with impunity, and that the permanent destruction of Japan was a real possibility. Even then, the Japanese government sought and won terms of surrender that were not entirely unconditional - the Emperor, after all, remained.

There was, of course, significant opposition within the United States to using the second bomb. Some of the bomb's own designers protested against its use, while the more practically minded worried if it was best to use the only other atomic bomb in existence to hit a city that posed no immediate military threat. Ultimately, the figurative smell of blood was too strong; the first blast had definitely surprised the Japanese command, and a second could finally, finally have a chance at ending a long a vicious war without a costly proposed invasion of the Japanese mainland.

Source: David M. Kennedy, Freedom from Fear.