Lots of interesting things to think about here.
What is the singularity? Well think about how fast computers are improving nowadays.
What happens when we build a computer that is capable of designing better computers than we ourselves are capable of designing?
What happens when that newly designed computer continues to propagate the process?
The capabilities of computers will increase exponentially from that point, so rapidly that it will take almost no time at all for the descendants of the original design to become unimaginably capable of processing information.
Of course this isn't a new or novel idea and it's explored in greater detail in the link provided but I thought it would be interesting to get some 'gut level' reaction from my peers. I particularly hope that some of you will follow the link to the short story 'Hard Takeoff' and let me know what you think about it. Even though it's so fantastical as to seem like pure fantasy I also can see the clear steps that might result in just such an occurrence.
The only detail that might not be accounted for is the energy requirements.