The technological singularity is a point in time coming sometime in the relatively near future in which we'll see the creation of superhuman intelligence through technological means. Popularized by science fiction writer Vernor Vinge (who coined the term) and futurist and inventor Ray Kurzweil, the technological singularity presents a huge challenge to science fiction writers who want to tell stories about the future.
The very nature of the technological singularity means it's impossible to predict what life will be like once said singularity occurs. Implications range from true artificial intelligence, with computers operating at faster speeds and greater efficiency than the human brain, to more advanced space travel, to the possibilities of incredibly long (possibly immortal) life spans for human beings. Most science fiction taking place in the future hasn't truly dealt with the implications of the technological singularity, but that's not all that surprising. Again, it's hard to write about something that's impossible to predict.
People have a hard time thinking about the possibilities of future technological advancement because our brains process such thoughts in a linear fashion. But technological advancement doesn't happen linearly; it's exponential.
Most singularity proponents think the event will occur sometime in the 21st century. Kurzweil, in his book, The Singularity is Near, puts the date around 2045, at which point he believes a $1000 computer will be a billion times more powerful than the combined sum of all human intelligence today.
My original plan was to set my upcoming novel Sacrosanct in the 22nd century (because, in my linear way of thinking, I didn't think technology would be at the necessary stage for the events of the book until at least 150 years from now), but after thinking about the implications of the technological singularity, I'll be moving the date up quite a bit.