What, Exactly, Are Black Holes?

The simple explanation that almost any idiot can understand: a black hole is basically a massive amount of matter compressed into a tiny, tiny little ball.

A little more in depth: Black holes are the remnant of stars that have gone supernova and collapsed upon themselves. When the star explodes in a supernova, not only does it explode outwards but it pushes inwards on its own core as well. The pressure placed on the core causes it to implode upon itself, and that's where the black hole is formed. However, black holes are only formed by stars large enough to create one... for instance the sun, everyone's favorite star, will likely not become a black hole once it goes nova. A star 10 times the size of our sun probably will, depending on how much matter is lost in the supernova. Only those huge stars have enough gravity to create a black hole.

Image courtesy of Scientific Objectives for Integral Science

The black hole gets its name from its massive gravity levels. The gravity associated with a black hole is so great that not even light can escape from it. This absence of light will obviously make the black hole appear to be, well, completely black.