The idea, widely held by the Extrop Ian crowd, that the curve of the total knowledge of humankind will continue to accelerate (Knowledge Growth) until it goes roughly vertical, at which point we will transcend humanity itself. Or something like that.
Here's the Vernor Vinge essay: http://www.ugcs.caltech.edu/~phoenix/vinge/vinge-sing.html
Robin Hanson coordinated some critical discussion among 13 people (in 1998): http://hanson.gmu.edu/vi.html
http://www.aleph.se/Trans/Global/Singularity/
http://www.extropy.org/ideas/lextropicon.html
John Robb has a weblog about it. http://singularity.manilasites.com/
Ray Kurzweil refers to it heavily in the Age Of Spiritual Machines. And has a website to go with it.
John Smart has a site http://www.singularitywatch.com/
Also associated with Hans Moravec, see http://www.kurzweilai.net/meme/frame.html?main=/articles/art0151.html
http://fusionanomaly.net/singularity.html
Terence Mc Kenna was into this as well, targeting 2012 as the expected date for Timewave Zero (based, among other things, on the Mayan calendar).
note many freaking things are predicted for this year
Others think the whole thing is a crock.