Black holes are the densest, most massive singular objects in the universe. Formed in one of three main processes, they exert so much gravitational force that nothing - not even light - can escape their pull. Since nothing can ever come out, it is called a hole. Since not even light nor other electromagnetic radiation can escape, it is called a black hole.
A black hole can be formed in the manner described above, but also in two other ways. The first is that if a star has more than nine solar masses when it goes supernova, then it will collapse into a black hole. The reason that a neutron star stops collapsing is the strong nuclear force, the fundamental force that keeps the center of an atom from collapsing. However, once a star is this big, the gravitational force is so strong that it overwhelms this force and collapses the atom completely. Now there is nothing to hold back collapse, and it collapses into a point (or, in theory, a ring) of infinite density. Stephen Hawking proposed a third way a black hole could form, theorizing that trillions were produced in the Big Bang with some still existing today. This theory is not as widely accepted.
The infinite density of the black hole causes such a strong gravitational well that not even light can escape from it. Since nothing can ever come out, it is called a hole. Since not even light or other electromagnetic radiation can escape, it is called a black hole.
A black hole's anatomy is pretty simple. The hole itself is known as a singularity. This is the very center of the black hole, and is where the mass of the original star (and all acquired matter) lies. In a Kerr black hole (a black hole that assumes the star's core was spinning and had a magnetic field when it collapsed), the singularity is theorized to be ring-shaped. In a black hole that does not spin, the singularity is a dimensionless point of infinite density.
No one knows what the singularity is like. Some believe it looks like "quantum foam." Others disagree and think it is more solid. Whatever it is, it is governed by physical laws that are not yet understood. No one knows if an object drawn into the hole would smash into it, becoming part of it, or if it would somehow travel through it (as occurs in popular science fiction).
Moving out from the center, the next part is the inner event horizon. Between the inner event horizon and the singularity, space is believed to be relatively normal - except for the fact that all objects are drawn towards the singularity and cannot escape.
Next out is the outer event horizon. This marks the boundary at which the escape velocity is greater than the speed of light, and all known objects are drawn into the hole. This also marks the "outer edge" of the black hole; we cannot see into it, for no form of known radiation can escape the gravitational pull from this point inward.
The next part of the black hole is only present in a spinning black hole. The ergosphere is a region of space where all particles are drawn in a circular path that match the hole's rotation. However, within the ergosphere, matter and energy can still escape the hole's grasp. The outer edge of the ergosphere is called the static limit. This is the distance that matter must maintain in order to keep a stable orbit and not be trapped by the hole's rotation.
NOTE: The only physical part of a black hole is the singularity. The other parts mentioned are mathematical boundaries. There is no physical barrier called an event horizon, but it marks the boundaries between types of space under the influences of the singularity.
Other parts of a black hole are present only in "active" black holes. The accretion disk is matter that has been trapped in orbit around the black hole. It will gradually be pulled into the hole. As it gets closer, its speed increases, and it also gains energy and begins to emit light. This is the radiation that astronomers can use to determine how much the black hole "weighs." By using the Doppler effect , astronomers can determine how fast the material is revolving around the black hole, and thus can infer its mass. Most black holes that have been found usually weigh several million solar masses.
No black hole has actually been imaged in a telescope. Actually, this is in itself impossible because, simply by definition, one cannot see "nothing." A black hole can only be spotted by observing how the material around it acts (inferred in the method in the previous paragraph). Through this method, astronomers have observed many dozens of black holes; they usually are found in the center of galaxies, and some believe that every galaxy harbors a black hole in its center.
What would happen if you were to fall into a black hole? As the you approach the black hole, your watch would begin to run slower than the watch of your colleagues on the spaceship. Also, your comrades notice that you begin to take on a reddish color. This is due to the warping of space in the vicinity of the hole. Then, just before you "enter" the hole (pass through the outer event horizon), your friends would see you apparently "frozen" there, just outside the event horizon and to them, your watch would have stopped (if they could observe it). They would never see you enter the hole, because at that distance from the singularity, an object must travel at the speed of light to maintain its distance. Thus your dim, red image would stay frozen in their eyes for as long as the hole exists.
However, from your vantage point, as you enter the black hole, nothing has changed. As you look "out" of the hole, the universe still looks relatively normal. However, you are drawn towards the singularity, and cannot escape its grasp. At this point, modern physics does not know what would happen. The most likely outcome is that you are compacted into a miniscule size upon the singularity.
However, you would not actually survive the fall into the hole. The immense warping of space around the hole would cause a spaghettification effect - you would be pulled apart because your feet (assuming they went feet first) would be far greater than the force on your head, and they you would be pulled as one pulls dough into a rope. This would be rather unpleasant, as well as fatal.
The idea of a white hole is the opposite of a black hole, and is entertained more in science fiction than in actual science journals. Some believe it is the "other side" of a black hole. It is theorized to spew matter and energy out. A flaw in this theory, as many scientists have noted, is that the matter ejected from the white hole would accumulate in the vicinity of the hole, and then collapse upon itself, forming a black hole.