Not seeing an in-depth answer here, I will take a shot. In one sentence, the Soviet delegate wasn't there. To understand why, we need to briefly explain Chinese history up until that point. You may wonder why we're talking about China in a discussion of the USSR, the United States and Korea, but China is actually the fulcrum for the UN response to Korea.

China had been engulfed in a civil war since before the Japanese invasion, which continued for four years after the Japanese were defeated (the two sides agreed to cooperate to fight the Japanese, but only lip service was paid to this agreement). Mao Zedong's (Mao Tse Tung) Communists eventually won in 1949, having fought Chiang Kai-shek's Guomindang (Kuomintang) completely off the mainland. They fled to Taiwan and established the Republic of China, which still exists (and is not in the UN today, incidentally).

China's seat at the UN in 1949 was still occupied by the Republic of China (ROC), not the People's Republic of China (PRC), as it had been since 1945, when the ROC joined the UN. The USSR had recognized the PRC, as Stalin and Mao were buddies (as much as either could be buddies with anyone), and found it intolerable that the UN would not replace the Chinese delegate with a delegate from the PRC. On January 13, 1950, the USSR proposed this change, but was opposed by the United States, the Republic of China (naturally), and other U.S. allies, which defeated the motion. The Soviet delegate walked out in protest and did not return until August, 1950, by which time they had missed the June resolution condemning North Korean aggression etc. and an opportunity to veto UN intervention in Korea. They hoped this would force the UN to see things their way. It backfired. The USSR finally got their way in 1971 with the passage of Resolution 2758, which booted the ROC out and allowed the PRC in.

Sources: You can see Security Council Resolution 82 here. See also Carter Malkasian's The Korean War. This sequence of events is undisputed fact, however, and pretty much any semi-decent book or source on the Korean War will cover it, so take your pick if you want further reading.