Black holes are such extraordinarily compact objects they require a theory that involves general relativity (the theory of gravitation) and quantum mechanics (the theory of microscopic particles), in short a theory of quantum gravity.

The popular definition of a black hole is a region of space having a gravitational field so intense that no matter or radiation can escape. When the gravitational attraction of the mass at the center singularity is greater than the centrifugal force of a particle grazing the event horizon, the particle will be drawn into the black hole, never to escape.

The centrifugal force on a particle with mass m traveling around a circle with radius r at velocity v is ½(mv²/r). The gravitational attraction of a mass M at the center is GMm/r².

Equating these, and assuming v = c, the velocity of light, the Schwarzscild radius R = 2GM/c².

Jacob Bekenstein showed that adding a low-energy photon with a wavelength the size of a black hole would add an area one Planck-length squared to its event horizon.¹

Leonard Susskind argued that the photon adds one bit of lost (or hidden) information to the internal entropy of the black hole (i.e., in the singularity at it's center) and one bit of information at the event horizon. Susskind's "holographic universe" interprets the event horizon as a hologram of the lost (or hidden) information inside a black hole.

But the event horizon is not a material structure capable of storing information. As first described by Karl Schwarzschild and Albert Einstein in the 1920's, the horizon is simply an abstract mathematical surface where the pull of gravity from the condensed matter of the singularity at the center prevents anything, including light, from crossing the horizon and escaping the black hole.

The center singularity is said to be infinitesimal in size but infinite in density, so there is nothing but empty space in a black hole between the singularity and the event horizon. Any particle that entered the horizon will very rapidly fall to the center.

Stephen Hawking added four famous properties to black holes.

First was the idea that black holes have "no hair," that the event horizon is featureless.
This is strictly correct. No visible radiation is coming through the event horizon, but we will see that immense amounts of radiation are being produced by the extreme activity in the immediate vicinity of the black hole event horizon.

Hawking's second idea was the radical proposal that black holes are not so black after all, because they are radiating information. This needs careful explanation.

This second idea is that "virtual particle" pairs are appearing just outside the event horizon, with one particle going into the black hole and the other radiating away what is known as "Hawking radiation." Now there is a vast amount of radiative activity around all observed black holes, otherwise they would not be observable, only discoverable by their gravitational effect on their luminous neighbors.

For supermassive black holes at the center of galaxies, all this activity is caused by the vast amounts of intergalactic material falling into the black hole. These active galactic nuclei were first detected as "quasars" or quasi-stellar sources. The largest are today called "blazers." These are the most powerful and brightest objects in the universe.

Hawking's third idea was that his radiation would be evaporating a black hole. This needs very careful examination. First, there is no evidence that black holes are evaporating. All observed black holes appear to be growing, fed by the intergalactic material they are accreting. Even that single virtual particle Hawking saw falling in (as its partner radiates away) does not reduce, it adds to the black hole mass. We can note that Hawking's pair production might be happening inside the event horizon a short distance. As long as the gravitational red shift is not enough to reduce the energy to zero, a weakened photon can pass through the event horizon.

The second law of thermodynamics suggests that even black holes that are currently unobservable are also growing and not evaporating. The intergalactic material is very sparse and very cold, warmed only by the 2.7K cosmic background radiation. But a black hole singularity is thought to be much, much colder, perhaps a millionth of a degree Kelvin. Heat flows from hot to cold, carrying the atoms of the intergalactic medium (perhaps as little as a few hydrogen atoms per cubic meter) into the black hole.

Hawking's fourth idea, and perhaps most important, was that information is being lost to the black hole. This is very likely correct

But multiple physicists claimed Hawking was wrong. Some made bets.

Susskind described this as the "black hole war" which, he said, was fought to "make the world safe for quantum mechanics." His argument was based on the argument that "information never dies." This is a "law of physics that may be even more fundamental than energy conservation. It's sometimes called reversibility, but let's just call it information conversation."².

1. The Schwarzschild radius is the radius of a spherical boundary around a massive object; if the object's entire mass collapses within this radius, it becomes a black hole. This boundary, also known as the event horizon, is the point of no return, where the escape velocity equals the speed of light. The formula for the Schwarzschild radius is R = 2GM/c² where G is the gravitational constant, M is the mass of the object, and c is the speed of light.  
2. Susskind, The Black Hole War, p.87