Mathematicians and physicists use "singularity" to describe a point at which an equation or model runs down the rabbit hole of infinity -- in the heart of a black hole, for example. So it made sense that the technological singularity popularized by Vernor Vinge would describe a future moment when computers, artificial intelligences or human intellect boosted by drugs or technology would zoom into uncharted, here-be-dragons territory. Depending on your viewpoint, it's inevitable or impossible -- a future to embrace or fear, assuming data density limits and the laws of physics don't preclude it.
Then again, maybe it's not a future at all. We already use computers to solve problems too big for us to comprehend in their entirety. We have developed neural networks, learning machines, and AIs like Watson capable of understanding language to a remarkable degree. The Internet, combined with augmented reality devices like Google Glass or even cell phone apps, already enable humans to vastly exceed their own mental capacity for memory and calculation -- although some argue that it also makes them dumber in the process.
Is the singularity already here? If not, who knows where technologies currently under development, including quantum computing and biochemical nanomachines, might lead?