The Singularity is the moment in human history when things go non-linear because of the ability to upload consciousness to computers. Hitching human intelligence to PC industry's growth curve will make incomprehensible transhumans out of us, rupturing history. It's a lot of fun for science fiction writers to write about.
Charlie Stross — who is all over this year's Hugo Ballot for a ton of fiction about the Singularity and other topics — has created a Wiki for mapping out the contours of the Singularity.
If you live through the SIngularity and you do not try UpLoading and are not rendered PostHumous by feral calculators or get eaten by GreyGoo, you may be one of the PostHumans. PostHumans are humans who are not human any more. Some of them work for the Post Office, which keeps track of the PostHumans and sees that they do not cause outbreaks of GreyGoo, but the rest of them live a leisured life, pampered and cosseted by their UtilityFog and BushRobot an' other frightful servitors. Bein' PostHumans looks wonderful from here, much like being a late 20th century Accounts Clerk or Call Center Worker would have looked for a Hungarian peasant in 1420 with the nobility trying to kill them, i.e. grey, boring, and extremely well-fed. Only it'll be more exciting than that because we'll have World of Warcraft 21.499! Or something even better to play!
PostHumans are all inhumanly handsome or pretty, live infinitely long, get free unlimited resurrections if they're killed by dire boars or feral calculators or eated by Buick-eating aliens, and they get to have magic PixieDust NanoTechnology skillz. Being PostHumans is the bizniss.