Why did Japan surrender in ww2 after the two atomic bombs?

Japan was already in the process of trying to negotiate a surrender. By August 1945 it was clear to everyone that Japan was losing. But the leadership thought they could get a better negotiated surrender, instead of the unconditional surrender the Allies were demanding. The primary hopes were that Japan could demand that it wouldn't lose any territory in the home islands, that the home islands wouldn't be occupied, and that the government could continue as it was.

They were trying to open these negotiations using the Soviet Union as a intermediary. Japan at the time wasn't at war with the Soviets. But August 9th changed everything. First the U.S. dropped the second atomic bomb. Then the Soviets declared war on Japan.

The U.S. demonstrated that Hiroshima wasn't a fluke. Japan couldn't know how many bombs the U.S. had or how quickly they could replace them. But what they did know is that the U.S. could now wipe out a city with four planes instead of the thousand odd planes it took to firebomb Tokyo. And could apparently do it every three days or so. Of course U.S. production hadn't really ramped up yet. But they were planning on a production rate of about 5-10 days per atomic bomb. And while that was going on the fire raids could also continue.

And on the same day the Soviets attacked, and began annihilating, Japan's largest remaining armies. By the time fighting ended (about a week after the surrender) Japan had lost over 700,000 casualties. The Soviets had also occupied Sakhalin, and the Kuril Islands, as well as parts of Korea.

So in the week before the surrender the U.S. demonstrated that they could destroy the islands without the need for an actual invasion. And at the same time the Soviets closed off their best hope for a negotiated peace, while simultaneously capturing and cutting Japan off from most of their remaining sources of raw materials and a huge part of their army. It was a one-two punch that even the most pro-war members of the cabinet couldn't ignore.

But it should be pointed out that even then the militarists in the cabinet had to be dragged to surrender over their protests. Toyoda said in the final meeting, "We cannot say that final victory is assured, but at the same time we do not believe we will be defeated." It took the direct intervention of the emperor to get them to agree. Even then several senior officials killed themselves rather than participate in the surrender. And there was an attempt at a coup to prevent the government from surrendering.

Sources:

John Toland's The Rising Sun
Ronald Spector's Eagle Against the Sun.