One simple explanation for Reiki is that it's a restorative healing technique, first introduced in Japan by a man called Mikao Usui in 1922.
More specifically, on the 21st day of a meditative retreat, during which Mikao fasted, he experienced an enlightening sensation, after which he noticed he had 'healing hands'.
Mikao went on to develop his new found gift, and share it with the wider community by opening healing centres and a school from which to teach others how they too could harness Reiki.
Personally I have found Reiki to be more than just hands-on healing, whilst this is a truly fantastic aspect, it has also opened up new, personal insights that I was previously unaware of.
Ideally Reiki is shared by a fully qualified practitioner who develops their skill over time by continuously learning the deeper aspects of this art form.