When we speak of black holes and their associated singularity, why is matter drawn into a black hole condensed into a single point within the singularity?
I seem to be answering a lot of questions about black holes at the moment!
In my answer to Why is matter drawn into a black hole not condensed into a single point within the singularity? I explained how matter falling into a black hole reaches the event horizon, and in my answer to Why is a black hole black? I showed how matter that reaches the event horizon can never escape it. So combining these two shows that once you've fallen into a black hole you can never escape. If you are prepared to restrict yourself to radially infalling matter then my answer to Why is a black hole black? shows that matter must hit the singularity because once inside the event horizon even light has a negative radial velocity i.e. even a light beam can't escape the singularity.
However that isn't the same as showing that once you've fallen into the black hole you are inevitably drawn into the singularity, because you might argue you could orbit the singularity. The proof that anyone falling into a black hole must hit the singularity was given by Hawking and Penrose. Unfortunately my mission to make GR understandable hits a problem here because I don't understand the Hawking Penrose theorem so I certainly can't explain it to anyone else.
To make life more interesting, if the black hole is electrically charged (Reissner–Nordström metric) or spinning (Kerr metric) it is possible to find timelike paths that do not hit the metric but instead lead back out of the black hole into another region of spacetime. I even ranted on about this as well, see Entering a black hole, jumping into another universe---with questions.
I think the explanation of colapse is due to Schwarzschild; you can find it in Wald's book, the chapter on Schwarzschild's solution. Very briefly, solving the Einstein's equation inside the massive star yields an infinite pressure at the center (above some mass threshold) with the only imaginable consequence being the colapse into a point. This all is solid only for the simple case of a spherically symmetric black hole, but I guess the qualitative feature is the same for all massive enough bodies which become a blackhole. And the matter drawn inside the horizon can not be differentiated from the blackhole anymore; it's part of the blackhole and sooner or later gravity destroys any structure it may have, near the infinite pressure center.