The Singularity is the theory that tehcnological advances occur at an exponential rate... you know, doubling every thousand years, then every 500 years, then every 250 years, etc.
Now it's at the point where it's doubling every 10 years or so, soon to be 5 years, then 2.5 years, etc.
At some point, (estimated to be within 30 years) It will start doubling at a rate that will start surpassing human comprehension- doubling every year, every six months, doubling every week, every day, every minute...
The day after it doubles every day is going to be an interesting day. Singularity people believe that it will really take off when artificial intellegence gets good enough to start learning on it's own.