1. The first comment on this article: The singularity refers to the time in human history when computers first pass the Turing test.
2. Wikipedia: A technological singularity is a hypothetical event occurring when technological progress becomes so rapid that it makes the future after the singularity qualitatively different and harder to predict -- hey, y'know what I call the point beyond which the future is hard to predict? I call it "the present".
... and I'm too lazy to keep looking up other definitions, but they're definitely out there.
The second problem with the idea is that some folks seem to have this flawed logical chain in mind:
1. Assume that a human brain can make a computer smarter than itself.
2. In that case, the computer smarter than the human can make a computer smarter than itself, which can in turn make a still smarter computer, and so on, leading to vastly smarter computers very quickly.
This ignores the fact that if we ever do make a computer smarter than a human it will either be via (a) reverse-engineering of the human brain or (b) some kind of evolutionary algorithm. The slightly-smarter computer is then no more capable of building an even-smarter computer than we are, since it also has to fall back on one of these two dull mechanical processes.