So let us begin our investigation with an explanation of what Reiki is and how it works.
The body is composed of energy. This has been scientifically demonstrated. This energy has been measured around the body, as well as photographed through Kirilian photography. This energy makes up the body, and also pervades it in more subtle forms. This energy, sometimes called the "aura", corresponds to the health of the body, as well as the state of emotions and mental activities.
Reiki, like Chinese medicine and other Eastern models of wellness, believes that imbalances in the energy field correspond to various levels of illness. The energy becomes imbalanced first in the energy field, and later manifests as illness or imbalance in the physical body or the emotional and mental health of the individual. Reiki seeks to rebalance these energy fields in order to restore health to the individual at all levels.
How does Reiki do this? Reiki practitioners are attuned to higher vibrations of energy that correspond to healthy states of being, as well as higher states of consciousness (as defined by spiritual advancement techniques such as yoga and meditation). Reiki practitioners are trained to become channels for these higher vibrational energies and during a session they bring these energies into the energy field of the recipient. When these strong vibrations are introduced, the recipient's energy field also begins to vibrate at those frequencies. This is much like a tuning fork being struck and the same note on surrounding instruments would be triggered. The higher vibrational frequencies then "correct" and balance the energy field of the recipient.
This explanation is a somewhat scientific or medical model way of explaining what is happening. It can be summarized by saying that the "bad" energy is removed and replaced with "good" energy. You can think of the energy field being "cleaned" of "garbage" allowing it to flow freely. Think of the energy system like a stream or river, and understand that "trash" will pollute it and will sometimes cause dams and prevent correct flow. Reiki opens the flow and cleans out the garbage.
At this point, the rational mind can say "Yes. That makes sense. I could understand how that would work and how it could help. But is it real?" This takes us to the next phase of our investigation: experiencing it directly.