Black holes, as far as we know, are only theoretical masses in the universe.  Simply, they are dead stars that collapsed under the pressure of gravity.   Black holes are extremely dense and nothing escapes their grasp, not even electromagnetic radiation.  Light can enter them, yet it can never escape, thus that is why they are named black holes.

The person to come up with the black hole theory was German astronomer Karl Schwarzschild.  In 1916, using Einstein's theory of relativity, Schwarzschild came up with what a black hole was, how it was formed, and what the components of it were.
 

If there were a picture of a black hole, this is what it might look like.

Black holes are made up of two parts, the singularity and the event horizon.  The singularity is the black part, the vacuum.  The event horizon is the sphere that covers the singularity, the it acts as a boundary for the black hole. When the horizon is electrified it is called an ergosphere and causes the matter inside the black hole to rotate. The horizons radius depends upon the mass of the singularity times the mass of the body in solar units(mass divided by the mass of the sun).  If any star is two or three solar units greater mass than the sun, then it is almost a definate chance that it will become a black hole.  What happens is that gravity tries to pull the particles of the star together, but creates so much pressure that the particles cannot take it, and simply die, or compact.  Time near a black hole is severly altered.  When approaching one time begins to slow down, and when right next to it, or in it, time completely stops.  Once an object is inside a black hole it becomes a object of infinite density without any dimensions.

There is evidence of a black hole in the star system Cygnus X-1.  The reason astronomers believe this is because when using the doppler effect, there is a shift in the pattern that shows an object 10-15 solar masses that is emitting X-rays.  X-rays are normally only emitted from a hot gas disk from a star that has been compacted.  Also, black holes can only be detected if it is gathering up matter, because that is the only time the hot gas disk is detected.  When stars compact, they do not always form black holes.  The first thing they can do is shrink into smaller objects called white dwarfs, which are about the size of the earth.  The second thing is shrink into a neuron star, about 20 miles in diameter, and third they can continue to shrink until they become black holes.