Here is an in depth definition, taken from Wikipedia:
The Technological Singularity is the hypothesized creation, usually via AI or brain-computer interfaces, of smarter-than-human entities who rapidly accelerate technological progress beyond the capability of human beings to participate meaningfully in said progress. Futurists have varying opinions regarding the time, consequences, and plausibility of such an event.
I. J. Good first explored the idea of an "intelligence explosion", arguing that machines surpassing human intellect should be capable of recursively augmenting their own mental abilities until they vastly exceed those of their creators. Vernor Vinge later popularized the Singularity in the 1980s with lectures, essays, and science fiction. More recently, some AI researchers have voiced concern over the Singularity's potential dangers.
Some futurists, such as Ray Kurzweil, consider it part of a long-term pattern of accelerating change that generalizes Moore's law to technologies predating the integrated circuit. Critics of this interpretation consider it an example of static analysis.
The Singularity has also been featured prominently in science fiction works by a plethora of authors.