It didn't, it was just another bombing raid among many as far as the Japanese government was concerned. It was the entry of the USSR into the war against Japan that ended the war (Japan had been hoping that the USSR would act as a go-between to negotiate peace until that point).
the entry of the USSR into the war against Japan that ended the war
It is impossible to disentangle the events. The Soviets declared war on Aug 8, Nagasaki was Aug 9, surrender was proposed by Japan on Aug 10. It was the totality of events that finally caused Japan to surrender. The Japanese Supreme Council was split on surrender even after Nagasaki and USSR invading Manchuria.
Here is a quotation from Seal Kido, who was a leader in the peace faction in Japan.
On the eve of the atomic attacks, the peace faction’s influence was becoming strong enough to constitute a counterweight against the war faction; and the atomic bombs drastically reduced the sway of the war faction, and the peace faction gained momentum. In addition, the Soviet declaration of war further reduced the dominance of the war faction and gave the peace faction the upper hand. Therefore, I think that the atomic bombs alone could have allowed us to terminate the war. However, the Soviet Union’s entry into the war certainly made it easier [for us]. It is difficult to tell which event contributed more to the termination of the war: the atomic bombs or the Soviet Union’s declaration of war.
...though, at the time?
After several years of war, across the globe, I can understand a messy end.
I can only commend the decision, from afar, as I am pretty sure the Japanese may not have surrendered so soon. And that's an awful lot of atrocities avoided, as well further military and civilian casualties.
//off topic: plus plus to the current Japanese government, and their support for Ukraine.