Spectrum has a Special Report on the Singularity up on their site. Wikipedia has a handy basic definition of technological singularity:
The technological singularity is a hypothesised (sic) point in the future variously characterized by the technological creation of self-improving intelligence, unprecedentedly rapid technological progress, or some combination of the two
A vague definition that only scratches the surface of the varied theories and ideas behind the Singularity, but suitable as an introduction. Popular films like The Matrix and The Terminator series reveal some dangers of the Singularity while Richard K. Morgan’s Takeshi Kovacs’ novels (Altered Carbon, etc.) focus on the immortality aspect of human consciousness transformed into something resembling a software program housed in hardware (i.e. our body).
In truth, at least as I see it, the concept (or theory if you prefer) is a weird intersecting of disparate sciences and philosophies that is fused into something that almost resembles religion; or spirituality at the very lest. Viable or not it makes for interesting discussion and even more interesting fiction.