There are many correct answers here.
But I am taking a different approach and considering the history of attempts to answer this question, which so far has not been found The answer was satisfactory in 1938.
At the beginning of the 19th century, the most widely accepted answer was that the origin of solar radiation was a reaction chemistry. energy production. Knowing the mass of the Sun and using the chemical reactions of the best-known energy sources, it is estimated that the Sun can only burn for about 5,000 years. At that time, the Earth was assumed to be several thousand years old, so this was not a problem.
But since the end of the 18th century, geologists have. .. .After finding evidence of sedimentary deposits and studying the sedimentation, he concluded that the Earth was much older, millions of years, tens of millions, hundreds of millions.
In 1862, William Thomson (Lord Kelvin after 1892) provided a new explanation for the Sun's heat: gravitational contraction. At the current rate of solar production and at the upper limit of its "initial radius" (Earth orbit), it has reached an age of 20 million years.
This was consistent with the youngest ages considered by geologists and also with their own estimate of the Earth's age, based on the time it took for a molten ball to form the present crust. However, Thomson's estimate of the "age of the Earth" was completely wrong because he did not take into account convection within the core and mantle (nor did he know about radioactive heating, an additional factor that also undermines his model, but this does not it is the case). because his answer was fundamentally wrong: it was wrong even according to the physics of the time).
But the proof that the Earth was much more than 20 million the elderly inhabitants were there and continued to accumulate. above (a little joke about sedimentation). For hundreds of millions of years nothing seemed plausible, so the source of solar energy remained a complete mystery.
The discovery of radioactivity in 1896 provided something of an explanation . Here we had evidence of a mysterious source of energy in the atom (or some atoms) that was about a million times greater than chemical energy. This suggested that the energy source was a process similar to radioactive decay, but no one could say what the process was.
Radioactivity also made new types of dating possible. of rocks, and it was soon discovered that the Earth must be several billion years old.
In 1920, in his short paper "The Internal Constitution of Stars", Sir Arthur Eddington postulated, using recently measured nuclide masses, that a process of fusion of hydrogen into helium (which was not found on Earth until 1895) explains energy. . Production, since the combination of four hydrogen atoms into a single helium atom would release a large amount of energy from the missing excess mass, and it was known from spectroscopy that the main elements of the Sun were hydrogen and helium. But the actual nuclear reactions through which this might occur were unknown.
Eddington developed this original idea in his 416-page treatise, also called "The Internal Constitution of "the stars are called." » published in 1926. In this extraordinary work he deduces the structure of the stars without knowing the reaction that moves them.
Two comments that Eddington says in the well-observed World Books:
“We would say that the arrangement of 4 hydrogen nuclei and 2 electrons to form the helium atom is impossible unless we knew this had happened."
"We can also look forward to the development of Heisenberg's new quantum mechanics."
It was not until 1937-1938 that Hans Bethe wrote his Nobel Prize-winning paper using this "new quantum mechanics", in which he explained the steps of the solar fusion process in two papers. The first described the proton-proton chain reaction, which provides 16.68% of the sun's energy. And in the second, the main source of solar energy was described: the CNO (carbon-nitrogen-oxygen) cycle, which provides 83.32% of solar energy.
Read Also : What do programmers and computer scientists know that most people don't?
Ola Hansen 
There are many correct answers here.
But I am taking a different approach and considering the history of attempts to answer this question, which so far has not been found The answer was satisfactory in 1938.
At the beginning of the 19th century, the most widely accepted answer was that the origin of solar radiation was a reaction chemistry. energy production. Knowing the mass of the Sun and using the chemical reactions of the best-known energy sources, it is estimated that the Sun can only burn for about 5,000 years. At that time, the Earth was assumed to be several thousand years old, so this was not a problem.
But since the end of the 18th century, geologists have. .. .After finding evidence of sedimentary deposits and studying the sedimentation, he concluded that the Earth was much older, millions of years, tens of millions, hundreds of millions.
In 1862, William Thomson (Lord Kelvin after 1892) provided a new explanation for the Sun's heat: gravitational contraction. At the current rate of solar production and at the upper limit of its "initial radius" (Earth orbit), it has reached an age of 20 million years.
This was consistent with the youngest ages considered by geologists and also with their own estimate of the Earth's age, based on the time it took for a molten ball to form the present crust. However, Thomson's estimate of the "age of the Earth" was completely wrong because he did not take into account convection within the core and mantle (nor did he know about radioactive heating, an additional factor that also undermines his model, but this does not it is the case). because his answer was fundamentally wrong: it was wrong even according to the physics of the time).
But the proof that the Earth was much more than 20 million the elderly inhabitants were there and continued to accumulate. above (a little joke about sedimentation). For hundreds of millions of years nothing seemed plausible, so the source of solar energy remained a complete mystery.
The discovery of radioactivity in 1896 provided something of an explanation . Here we had evidence of a mysterious source of energy in the atom (or some atoms) that was about a million times greater than chemical energy. This suggested that the energy source was a process similar to radioactive decay, but no one could say what the process was.
Radioactivity also made new types of dating possible. of rocks, and it was soon discovered that the Earth must be several billion years old.
In 1920, in his short paper "The Internal Constitution of Stars", Sir Arthur Eddington postulated, using recently measured nuclide masses, that a process of fusion of hydrogen into helium (which was not found on Earth until 1895) explains energy. . Production, since the combination of four hydrogen atoms into a single helium atom would release a large amount of energy from the missing excess mass, and it was known from spectroscopy that the main elements of the Sun were hydrogen and helium. But the actual nuclear reactions through which this might occur were unknown.
Eddington developed this original idea in his 416-page treatise, also called "The Internal Constitution of "the stars are called." » published in 1926. In this extraordinary work he deduces the structure of the stars without knowing the reaction that moves them.
Two comments that Eddington says in the well-observed World Books:
“We would say that the arrangement of 4 hydrogen nuclei and 2 electrons to form the helium atom is impossible unless we knew this had happened."
"We can also look forward to the development of Heisenberg's new quantum mechanics."
It was not until 1937-1938 that Hans Bethe wrote his Nobel Prize-winning paper using this "new quantum mechanics", in which he explained the steps of the solar fusion process in two papers. The first described the proton-proton chain reaction, which provides 16.68% of the sun's energy. And in the second, the main source of solar energy was described: the CNO (carbon-nitrogen-oxygen) cycle, which provides 83.32% of solar energy.
Read Also : What do programmers and computer scientists know that most people don't?