Hawking radiation describes hypothetical particles formed at the boundary of a black hole. This radiation tells us that the temperature of black holes is inversely proportional to their mass. In other words, the smaller a black hole, the hotter it will glow.
Although never directly observed, Hawking radiation is a prediction supported by the combined models of General Relativity and quantum mechanics. The reason why this radiation is called "Hawking Radiation" is because in 1974 the great physicist Stephen Hawking "Black hole explosions?" ("Black Hole Bursts?") is the first to question whether such radiation could exist.
Why Should Black Holes Glow ?
When matter enters a black hole, it is now completely isolated from the rest of the Universe. Before Hawking, scientists thought that objects falling into a black hole could never escape, so black holes were a one-way street. According to them, black holes radiated no matter, energy or information. However, this also means that the measure of disorder that physicists call entropy disappears. This property of black holes was thought to violate the second law of thermodynamics, since the destruction of matter within black holes would make the Universe less disordered (or more ordered).
Hawking disagreed with this view. According to Hawking, black holes obeyed the second law of thermodynamics and their entropy had to increase with time. This is a critical admission; because everything that has entropy has to have a temperature! In other words, entropy is just another way of describing heat energy that always emits radiation. If the event horizon had entropy, it should glow somehow. So black holes couldn't be that black.
But Hawking wasn't the only physicist trying to solve the black hole problem. Jacob Bekenstein, a physics student at Princeton University at the time, showed that when matter falls into a black hole, the surface area of the event horizon, which is the region most affected by the black hole's incredible gravity, must grow somewhat. He showed that this change in surface area was equivalent to entropy that would otherwise have been lost, and this suggestion could have resolved the paradox.
However, Hawking wasn't too sure about this explanation either. For this reason, Hawking tried to determine the temperature of black holes with his calculations. To do this, he combined Einstein's Theory of General Relativity, which explains how gravity works at large scales, with the predictions of quantum mechanics, which describes how the Universe works at the smallest scale. These two theories are still not combined today, and one of the biggest dreams of physicists is to reach the Theory of Everything, which can explain the Universe from the smallest to the largest in one go. Hawking had to take advantage of both these theories; because both theories allow us to explain how things work in the event horizon of black holes.
In his efforts to refute Bekenstein's seemingly absurd proposal, Hawking discussed the issue with other physicists and tried using mathematical models to show that it was not possible. But far from disproving Bekenstein, Hawking found that black holes do indeed shine with a kind of cold light. He even delivered it to the masses with these immortal sentences:
"Black holes are not eternal prisons as we once thought. Something can escape from black holes; both to the outside and maybe to other universes... So if you feel like you're in a black hole, don't give up. There is a way out!"
Result
Ultimately, Hawking's theory shows how the convoluted fabric of space-time twisting around black holes can disrupt the mixing of quantum properties in areas near the event horizon. So much so that while black holes scatter some features, they can keep others intact. These properties are similar to the specific temperatures of the radiation, which we call radiation, and cause black holes to shrink over time.