What is the technological singularity?

I'm reading about the concept of the technological singularity on Wikipedia, just trying to get my head around it. I think the idea is that technology starts advancing so quickly that it represents a fundamental break in the nature of the world. Cory Doctorow described it in an interview as "things getting better and better until they burst".

It's hard to squeeze a big concept like this into my tiny brain. It seems to me that the world would grow an extra dimension. You need to see something like that from an outside perspective to make sense of it, and the only way to explain that from my point of view is from totally outside the three spatial dimensions as we know them.

If you look at the number of blades on disposable razors (stick with me, it's from the Wikipedia article), it's increasing exponentially. Extend it onwards into the future and you have infinite blades by 2015. So what does that mean in practice? You can't fit infinite blades on a disposable razor, so it must be something else. Everything post-Singularity starts sounding like that: a totally logical but inconceivable notion.

The whole of this concept makes about that much sense. You start talking about crazy things like computers that build better ones faster than you can count the generations. By the time one is finished building the next, the third one is designed and running. You're standing between two mirrors and you see the reflections start to propagate, then accelerate, and then they all stack up and rush back to the mirror face and you're falling. You don't even know where you are any more, because the world has popped and it moves too quickly for you to keep up.

The concept of ascension as in the Stargate universe can be seen as a kind of singularity result. When your own earthly intelligence builds at a rate that exceeds the capacity of this universe, your mind bursts beyond it and you ascend to a higher plane. Your life there, though far beyond what lower mortals comprehend, is still mundane relative to the other denizens of that plane. I think that's the post-Singularity answer: it's huge, but once you're there it becomes mundane.

Mokalus of Borg

PS - I don't understand half of this.
PPS - I don't think I can.