“The Singularity” used here refers to the belief popularized by writer Ray Kurzweil in his book “The Singularity is Near” that at some future point in time Robot intelligence will exceed human intelligence (probably around 2045 AD.) and they will take over the reins of civilization. Hope that helps; if still curious get the book published by Viking.
It now appears that that may happen not because robots become super intelligent but because humans are rapidly becoming dumber.
Love it! I don't think it will happen in my lifetime, though. There is some theory (the name escapes me, 'Moore's law'?) that says computing power doubles every so many years, and that if graphed it shows that computing power will surpass the human brain at some point in the future.
Fascinating stuff.