Where does '350' come from?

Dr. James Hansen, of NASA, the United States' space agency, has been researching global warming longer than just about anyone else. He was the first to publicly testify before the U.S. Congress, in June of 1988, that global warming was real. He and his colleagues have used both real-world observation, computer simulation, and mountains of data about ancient climates to calculate what constitutes dangerous quantities of carbon in the atmosphere. The Bush Administration has tried to keep Hansen and his team from speaking publicly, but their analysis has been widely praised by other scientists, and by experts like Nobel Prize winner Al Gore. The full text of James Hansen's paper about 350 can be found here and pdf full text (18 pages).