Reiki is similar to the use of acupuncture in that it is designed to aid in the movement of bound up energies in the system.  The best way to explain Reiki is as an energetic transfer.  
Have you ever had someone walk into a room and just drained the energy from you...a so called energy vampire...you feel worse when you are around them?
How about the opposite experience with people that just always make you feel better when you are around them?
That's in large part due to an energy transfer that happens when you enter someone else's energy bubble.
Bear with me....let's talk science! Did you know that the energetic field and vibration of the human heartbeat can be measured about 6 feet away from the actual person! Instruments can pick up it's frequency and energetic influence from that far away!  Can you imagine then the impact if your body gets closer and closer to it?  Stepping in to that energy bubble has direct effects on your own system which is what we call an energetic transfer.  As you step into their bubble, you affect them, and they affect you.  Reiki uses this premise to bring energetic healing through learned manipulation of one's own energetic field.   Thus, Reiki is often done without the 'laying of hands',  which is sometimes super important for how the transfer takes place.  However, the healing power of touch (from hugs, to holding hands, to massage, to chiropractic) is very real, so we often incorporate that with chiropractic for an extra boost of healing!