Much has been written about the Technological Singularity since the concept was popularized by Vernor Vinge in The Peace War and Marooned in Realtime. Other writers include Ray Kurzweil and Bill Joy ("Why the future doesn't need us" in Wired). There have even been conferences on the topic.
The Technological Singularity has also been the subject of hundreds of science fiction stories, and has spawned a new sub-genre of SF called "post-Singularity".
The idea is simple: Moore's Law continues to lead to ever faster, smaller, cheaper, better computers. At some point, we'll create a computer smarter than the smartest human. When we ask that computer to design a still smarter computer, we cannot understand the resulting intelligence, let alone keep up with it. The "singularity" happens when the pace of innovation and improvement goes exponential -- we can't imagine what is on the other side of that event.
Many people seek The Singularity as the "rapture of the nerds". If people can be augmented by our technology (think bionic brain) with better memories, faster thinking, greater intelligence, then perhaps we can participate, perhaps we will transcend.
If we can download our minds into a sufficiently advanced computer then perhaps we can participate (I'll leave it up to others to decide if my downloaded duplicate personality is really me. Personally, I think I'll still be dead.)
However, many other people believe that humanity cannot participate in The Singularity, that it will rather be our offspring--highly advanced computers--that will benefit. Do read that Wired article, "Why the future doesn't need us". And be very, very afraid.
Personally, I don't see how humanity can participate in the Singularity. See my post, I am an optimist - we WILL have a future, for a discussion. Our computers may indeed have their Singularity, which will be disastrous for us even if we survive. I am writing a series of stories about the creation and evolution of a government agency dedicated to preventing a Technological Singularity, largely by restricting the creation and use of advanced Artificial Intelligence. But human nature is against us.
We must take drastic measures if we want humanity to own the future, and not our computers.