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In the center of each black hole is a singularity, a point where infinite density develops as spacetime approaches it. Spacetime goes toward infinite curvature and matter is crushed to infinite density under the pull of infinite gravity. At a singularity, space and time cease to exist as we know them and current laws of physics cannot be applied to this region.
Singularity form by a collapse of a star, where star with high enough mass (above 30 times the sun) would shrink under its own gravity and force until a single, one dimensional point. When it forms, space and time would be infinite in there.
An example would be that if a person is to stand on a collapsing star right before singularity form, and he sends a signal every second to a nearby observer, time and space would slow down as singularity is being formed, so that the observer would hear the signal slowing down. Let's say the singularity form at 12:00 exact, the observer would receive all the signals, one after another, with each successive signal slowing down at a very small rate, until the 12:00 signal, where time and space would be infinite to send a signal, in other words, forever.
To understand singularity, one would first have to believe infinite density, like how the original Big Bang started.Big Bang, most scientists believe, started from an earlier universe that was pulled together by gravity to a single point, at which it was then exploded to all the matter in the expanding universe. A black hole singularity is similar, except on a smaller scale. Imagine our sun decrease to size of the nucleus of an atom, it's very dense out there. However, our sun does not have high enough mass and is well below the Chandrasekhar limit, which means it will shrink to a white dwarf, with radius of a few thousand miles.
(Paragraph 3-5 Based on "Brief History of Time" by Stephen Hawking)
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