Physicists and philosophers asked themselves those questions for many centuries. Some were of the opinion that light consisted of tiny particles. Some other thought that it was a wave. For a long time these two theories contended against each other. In the 19th century it seemed that physicists at least settled the problem in favour of the wave theory. Many experiments have shown the wave structure of light. They have shown that it underwent diffraction and interference just like a wave (the famous Young experiment). It also extended that light was an electromagnetic wave. It seemed that Maxwell laws could explain all the phenomena of light and so it seemed that the wave structure was the right one.
But however Maxwell laws explained many of the phenomena of light, they didn't really explain them all. In 1905 Albert Einstein explained the photoelectric effect assuming that light consisted of some particles called photons. Soon there were more facts confirming the molecular theory of light. The problem appeared again; which theory was right- the wave or the molecular one?

The great Danish physician Niels Bohr suggested a solution conciliating both theories. He just came to the opinion that light had dual, wave - particle nature. In no experiment we see both characteristics at the same time. Sometimes light acts like a wave and some other times like a particle. To understand what light is one must take its both characteristics into consideration. Neither the theory of particles (photons) nor the wave theory of light are correct if considered alone. Only combining these two one gets a full and proper one.
Niels Bohr came to the opinion that light is both a wave and a particle. Physicians had treaded waves and particles separately before it became necessary to combine the both ideas of light into one. What more one can't imagine light duality. In the world of ordinary sizes where we live there is no equivalent to such duality. One can imagine a particle, and one can imagine a wave. But it is impossible to imagine something that is a particle and a wave at the same time. However that is the nature of light and we must accept that.

There is one more thing about the nature of light. It deals with the Einstein equation:
 

       

Scientists universally accept the dual character of light. However strange, it correctly describes known phenomena connected with light. Soon it extended that it was not only light to have a dual nature.