The Singularity is technological change so rapid and so profound that it represents a rupture in the fabric of human history. Some would say that we cannot comprehend the Singularity, at least with our current level of understanding, and that it is impossible, therefore, to look past its "event horizon" and make sense of what lies beyond.
It is also defined as the point at which a computer will pass the Turing Test for artificial intelligence in which a third party cannot distinguish between a human and the computer.
Ray Kurzweil (pt1of3) The Singularity Summit at Stanford
Ray Kurzweil - parts two and three are available at YouTube - they explain in greater detail the progress toward the singularity.
IBM is leading a group of researchers to build brain-like computers:
Plans are underway for a university without professors - but, with computers: