What is Singularity? Well it is kind of like a religion for nerds, if religion was based on scientific and technological research and advancement. Singularity is a movement of very smart people working towards technological immortality and/or doom.
Singularity is many things, but at the heart of it is always artificial intelligence. Why AI? Because the truth of the matter is human beings have real imposed limits based on biological evolution, computers do not have as many limits in terms of thier potential. For those who say that computers are limited by thier creators, for that I would say, for now that may be the case. Kurzweil is known for stating that God did not create man, but man has not created (or become) God YET.
The first and most likely singularity situation is Artificial Intelligence. At first AI was able to beat us in chess, now it is beating us at Jeopordy. Should we be afraid of AI? You should, since Singularity places the year 2050 as when AI will be double or triple the intelligence of humans, and not the dumb ones, the crazy smart ones. 2025 is when AI is as intelligence as human beings, though current AI is probably already significantly smarter than the average American as demonstrated by Watson and the number of people voting for Republicans.
You can think of every single AI driven armegedon as a possible outcome to this. Skynet, the Matrix, 2001, and I can go on. You know the story, though the likeliness of this happening is kind of complicated. The people who are involved in Artificial Intelligence branch of Singularity are very big fans of Asminov, in fact Asiminov may very well be the equivilent of Jesus Christ for real nerds. Isaac Asiminov was probably one of the major intellectual and literary forces during his lifetime. He wrote something like 9000 works of both fiction and nonfiction and only has one section of the Library of Congress system he is not published in, psychology, which is mildly ironic if you ever read the Foundation. He is also probably one of the best science fiction writers that ever lived. Basically he could probably go toe to toe with Tesla and Einstien, and outwrite every major fiction writer living, he was that smart. Getting back to the Singularity, Asiminov is probably best known for the three laws of robotics (which became four laws). To boil down the laws, it basically says robots may not harm humans or humanity, these laws likewise applies to AI, but only to a point. There is some theories if that this can even be controlled in such a way since the machine may become self aware enough to re-write its programming. This all becomes some very disastourous loop, so you may just well start getting ready to bow down to your computer overlords.
So you want to be a cyborg. Than my friend you are a bit perfect for the singularity. Because with the singularity you can get your ghost in the shell/borg/cyberman on. A possible outcome of the singularity is advanced cybernetics. Basically achieving evolutionary advancement through becoming more technologically integrated. Think this is not already happening, you are reading this on a computer being networked worldwide and recieving information augmenting your current reality through advanced technology. You think it is all to pump out cute cats that are bad spellers and porn. Instead it is the technological means to transition you to the Singularity. Some are reading this on your smartphone, if you are, you are even further along. So this is kind of already happening. We are unlike any human that has existed before in some ways since we are significantly more technologically integrated, and we will keep on advancing. This is changing us in some very real ways. It may sound like a bad Doctor Who plot, but we are well on the way to being cybermen.
This is the biological branch of singularity. It has to do with unlocking the genetic potential of human beings. This may extend life significantly as we turn off the dna that makes us age for example, it may also make us smarter as we tap into greater portions of our brain. Then again, it may also result in a future that is similiar to Gattaca. Out of all the Singularity possibilities, this is probably the single most boring since it does not involve the potential for robot or cyborg apocolypse. But it can involve a plague if we are not careful, but to be honest...that is not even remotely as interesting as the rest.
I will call this the Dollhouse-Caprica path. Since it evolves the brain mapping of Dollhouse with the virtual reality worlds of Caprica. Basically they scan your brain and upload it into an advanced network, thus allowing you immortality, and more than just simple immortality but the adbility to become significantly more intelligent as #1 may very well apply to this situation as well. This is the particularly awesome aspect of the singularity, if it does not lead to our doom by copying our new programmed based selves into humanity destroying robots. Why? Humanity evolves beyond our bodies and our intellectual capabilities evolve as well. This is at the heart of singularity, evolution through technology and science. Then again this can end up in some pretty nightmarish situations as well, since nobody is ruling out the Fail Whale and corrupted data, not to mention the general content of the internet.
Singularity and the concept of such involves many incredibly intelligent people which are probably significantly smarter than you will ever be and have done amazing things that your lazy ass will never accomplish. But no one looms larger than Ray Kurzweil in Singularity, well maybe Asminov, but he's dead. Ray Kurzweil is probably best known for making incredible synthesizers for Stevie Wonder and Trent Reznor (and countless other musicians). But he is also very big into publicizing the Singularity as well as consuming an inordinate amount of vitimans. He is trying to live long enough to be a lasting part of Singularity, whatever that may imply. He is also constantly meeting with other smart people to make his idea of technological evolution a reality. If Singularity were similiar to Sceintology (it's not), he would be it's L. Ron Hubbard. The difference is Singularity is a real scientific and technological movement that would make the creators of any previous technological endevors jealous, and scientology involves a bunch of celeberities and bad pseudoscience that makes nobody jealous.