This is probably one of the most biased, opinionated and/or extrapolated about in countless books, summaries and etc, ever since that Kurzweil fellow had a hand in bringing the term into more mainstream conversation or making it up to suite what he believes. Personally I find his approach to this supposed "technological singularity" a bit too idealistic, though his heart is in the right place despite as much. Anyways back to the singularity, I think a technological singularity is a misnomer at best, considering its description or what is usually associated with it is largely inaccurate when one considers that innovation and technology are not always so concentrated. The better term is not a singularity, but more of a technology paradigm shifting event(s) or just a plain paradigm shift will do, since we are a lazy nation.
It will be various steps forward and back in various fields, though the primary will be Nanotechnology, Biotechnology, Info-tech or Cognitive science (NBIC fields for short). Some of these fields can enable the others and vice versa, though I sincerely doubt all of them will get major leaps forward simultaneously...hence why I'd not call it a singularity since it is just a set of shifts in those fields/industries.
Those advances and steps forward will be the stuff of sci-fi, though I imagine it won't work how we picture it to work in such fictitious novels, as with anything...it might never meet our expectations or even potentially blow them out of the water. Example, one of the advances to come could be a near complete if not total understanding of the brain as well as why we have sentience...since consciousness is not a human trait. It could open whole new vista's, such as understanding and correcting Alzheimers with no ill effects, perhaps even build prosthetics for parts of the brain lost to one accident or another. The possibilities and roads we can go with that alone are mind blowing, but it is not without its limits and its own brand of ethos.The same goes for all the various other NBIC fields involved in the supposed singularity, they all will grant us possibilities and innumerable issues along with them.
After saying all that, I think the more pertinent question is not what is the singularity, as it's clearly being hyped and idealized, but are we prepared for what is to come? Can we honestly handle the eventual waves made by these shifts? What about laws? Regulations? What would be ethical or unethical?
The last and most important question that has been voiced so many times:
What does it mean to be human and would we still retain that after all is said in done?