Hmmm. To the best of my knowledge, the Korean peninsula wasn't the subject of any formal agreements at Potsdam. It may have been discussed informally as the hoped-for Japanese surrender was one of the major topics at hand, but certainly nothing was signed.

The 38th parallel is an example of the saying that a good compromise is supposed to leave everybody mad. Being blunt, neither the Soviets nor the Americans were particularly interested in sharing the peninsula, but neither was in a good position to control all of it quickly in the chaos surrounding the end of the Japanese empire. They agreed to divide Korea along an artificial border, the 38th parallel, at the suggestion of two American colonels in the Department of Defense (then the Department of War), Charles Bonesteel and Dean Rusk. (More on Rusk below; he's an interesting figure.)

Why? The Soviets and Americans' reasons for doing this were somewhat different, but at heart, the truth is that neither of them fully trusted the other, or wanted to get tangled in another conflict so soon after a massive war on two different sides of the world:

• The Soviets agreed to it because the bulk of their military (well, what was left of it after the European portion of the war drew to a close) was concentrated in Europe. They could move troops onto the peninsula from Manchuria and Siberia, but they couldn't bring significant reinforcements or naval resources to bear quickly if a big fight broke out with the Americans. By agreeing to divide the occupation zone at the 38th parallel, Stalin was guaranteed to get two warm-water (i.e., they don't freeze over in winter) ports on the eastern coast, Wonsan and Chongjin, without any further losses, and that was a significant strategic gain for him in East Asia. As an aside, Wonsan was actually the port that Kim il-Sung (later to become the effective dictator of North Korea) landed in on the return to his country.
• The Americans agreed to it because, even if they had masses of men and ships in the region, nobody could be spared for Korea for the better part of a month due to simple logistics and the enormous and immediate demands of the Japanese occupation. Truman was afraid that the Soviets would attempt to occupy the entire peninsula if given the opportunity to do so, and that the effort to evict them would quickly devolve into exactly the kind of nightmarish, bloody invasion that he had feared so much in Japan.

So in short, the Soviets had the element of speed on their side, but not the resources to control the entire peninsula effectively; the Americans had the men and resources necessary to control Korea, but couldn't do it quickly. Rather than risk open conflict, division of the occupation zones along the 38th parallel was an acceptable compromise, even if the border itself was kind of arbitrary and basically just picked because it split the country into fairly even halves. The later Korean War didn't change it much, although Kaesong did change hands from South to North Korea.

Unfortunately, I can't locate the actual date of the agreement. I'm sure I've got it in one of my books around here and I'll keep looking, but I can give you the rough time period. It's recorded as having been a quick, informal agreement that occurred between Japan's capitulation and formal surrender.

So as far as I can make it out, this is what you're looking at (all dates in the summer/early fall of 1945 obviously):

• August 6th: U.S. drops first atomic bomb on Hiroshima.
• August 8th: Soviets formally declare war on Japan.
• August 9th: U.S. drops second atomic bomb on Nagasaki. Soviet Union begins the Battle of Manchuria.
• August 15th: Japan announces its surrender. Soviet Union enters Pyongyang in the territory that will later become North Korea and encounters token Japanese resistance.
• ???: Agreement between U.S. and U.S.S.R. to divide Korean occupation zones along the 38th parallel.
• September 2nd: Japan signs formal surrender on the USS Missouri.
• September 8th: American forces land at Incheon (in what will later become South Korea).
• September 19th: Kim il-Sung returns to Korea.

Note: Rusk would later become Secretary of State under Kennedy and Johnson. He is likely the original source of a political swipe at the French that, many years later, made the rounds on the internet as something Colin Powell supposedly said or at least paraphrased. However, given his background, Powell is likely to have been familiar with Rusk's spat with Charles de Gaulle, as it concerned France's exit from NATO in 1966.

Source: The most immediately useful source I have for this is Bradley K. Martin's Under the Loving Care of the Fatherly Leader.