Black Holes
Members of a certain class of physical objects have a property known as the Schwarzschild radius. This class of objects includes (or is entirely occupied by - not sure) stars. The size of this radius is proportional to the mass within the object.
The occurence of black holes is a result of a star's state of collapse causing it to be smaller than its own Schwarzschild radius. When this happens, the Schwarzschild radius can be referred to as an event horizon and the star within it a "black hole".
For reasons unknown to me, any empty space on the inside of an event horizon causes space-time to bend in uncomfortable ways. Astrophysicists crapped themselves when they ran some of Einstein's equations over the event horizon scenario. It surely has something to do with the ridiculously high density of the object within. The specific outcome of this "bending" in space-time is that objects coming into contact with an event horizon are forced to move through time NOT through space. Objects can only move through time in the positive direction, and as it happens, the positive direction in this case is targetted at the centre of the event horizon sphere.
The understanding that black holes pull objects and light in because of their incredibly strong gravity is a myth and a simplification of the truth. Things don't fall into black holes because they are pulled by gravity. They fall into the black hole for the same reason that Thursday becomes Friday. Because time says you have to keep moving forward.
In a rather perplexing way, this rule also applies to the original star itself. So when the star collapses into the inside of its own event horizon, it is compelled by time to spontaneously collapse into a singularity. So, in a oddly theoretical fashion, the star officially obtains a radius of zero, and if you want to get mathematical about it, this means density is approaching infinity. (As if things weren't bad enough already).
There are a whole heap of suggestions as to what happens to objects captured by this bent sector of the continuum, but no real grasp of the situation. It is believed (well, by me anyway =) ) that objects being compelled toward a singularity are forced into the following conditions:
(a) Extreme acceleration
(b) velocity approaching the speed of lightTM, as a result of (a)
(c) mass approaching infinity and volume approaching zero as a result of (b)
A discussion of what happens to the object then can take a while. I've thought up some possible results, but I don't think they belong on this node.
That's my 0.02 cents.