In a nutshell, the Technological Singularity is a term used to describe the theoretical moment in time when artificial intelligence matches and then exceeds human intelligence. The term was popularized by scifi writer Vernor Vinge, but full credit goes to the mathematician John von Neumann, who spoke of "ever accelerating progress of technology and changes in the mode of human life, which gives the appearance of approaching some essential singularity in the history of the race beyond which human affairs, as we know them, could not continue."
By "not continue" von Neumann was referring to the potential for humanity to lose control and fall outside the context of its technologies. Today, this technology is assumed to be artificial intelligence, or more accurately, recursively-improving artificial intelligence (RIAI), leading to artificial superintelligence (ASI).
Because we cannot predict the nature and intentions of an artificial superintelligence, we have come to refer to this sociological event horizon the Technological Singularity — a concept that's open to wide interpretation, and by consequence, gross misunderstanding.
Via Szabolcs Kósa