The system of Reiki was developed by Japanese scholar Mikao Usui.
Born in 1865, he was partially educated in a Buddhist monastery, and developed a strong interest in spiritual matters at a very early age. He was also a keen martial arts practitioner - which may explain the emphasis on energy in the system of Reiki.
Besides pursuing various "worldly" careers throughout his life (as well as caring for a family), Usui dedicated much of his time to spiritual studies. Although a Buddhist throughout his life, he explored different traditions, including Tendai Buddhism and Zen Meditation, he seems to also have studied other religions. For a number of years he even was a Buddhist monk, although he was allowed to stay with his family.
It seems that he was looking for a certain, deeper spiritual connection within himself, something he had apparently read about in ancient scriptures, but grew disappointed as he could not find what he was looking for.
After years of intense search, he finally embarked on a long period of fasting and meditation where he came close to death. On the last day of this retreat, he suddenly felt a big change in himself - and had found the spiritual connection he had been looking for.
It is generally assumed that he meditated on Mount Kurama, near Kyoto, when he experienced this moment of enlightenment, or Satori, as the Japanese say.
It is said that on his way back from his retreat, he met a number of people with physical illnesses, and placed his hands on them in a gesture of comfort. To his great surprise, the symptoms got better.
He explored this more and more, and eventually realised that his spiritual awakening, or connection, came with the "side-effect" of physical healing.
Back in Tokyo, he started teaching his method of opening a channel for a spiritual connection with oneself - with great emphasis on meditation and spiritual growth. But he also started to offer healing to people.
This was the birth of the system that is now known as Reiki - all over the world.