Simply put, Reiki is an energetic healing system using the laying on of hands to channel energy from the universe into a person, place or thing with the intent of healing to wholeness, whatever that may look like. Reiki is a specific form of this healing support system. There are many more definitions of what Reiki is and isn't and you can find links at the bottom of this page for more information.
The practitioner is not the healer, but rather an open channel from which energy flows into and out of.