If you want to fast-forward through, the presentation proper starts at 0:31 and a compressed version starting at 3:52.
In it, Rosling shows quite graphically how the world began to shift from a demographc regime not that far removed from the high fertility/high mortality pattern experienced in the Roman Empire and in other traditional societies, Greater Europe with its industrialization proceeding while Asia and African stayed behind, with peak inequality occurring after the Second World War. It's at that point that the rest of the world began to converge with the developed world, first in health terms then in income. His suggestion that improved technology and increasing globalization will see this convergence continue--perhaps at least in demographic terms, if not economic--seems plausible on the face of it.
For more innovative statistical presentations on matters demographic, I highly recommend Rosling's Gapminder site. Go, peruse.