Mikao Usui, the story goes, was the founder of the Modern Reiki movement(s). Mind you that Usui specifically set out to uncover ancient healing methods. Thus, Usui was convinced that these methods were not "his" but that it was his obligation to disseminate this newly re-acquired information so that it would not be lost again.
Level I Reiki introduces the practitioner to basic healing energies mainly tuned to physical healing, and the practitioner is taught techniques for laying hands on a patient, and transferring the healing energies to the patient. That's about it.
Level II introduces the concept of different KINDS of Reiki energies, and one triggers them through the use of 3 Reiki symbols, which are mnemnomic links to the energy frequencies used for different kinds of healings. This level introduces emotional and spiritual healing, for instance. Also introduced are distance healing, and a concept of "Reiki guides" or an individual practitioner's helper spirits who are knowledgable in Reiki.
Some teachings of reiki divide Level III into two sections, so I'm splitting it up here just for ease....one part of Level III learnings give (2-4) more symbols, further practice, and new techniques for using Reiki. [This level of Reiki also includes learning to raise Kundalini power (search for websites on Kundalini and Tantric Yoga (tantra)), but I believe that's tangental, and may have been added in by Diane Stein to the basic picture of Reiki.]
The practitioner learns how to "attune" new Reiki practitioners to all the levels of Reiki, as well as the approved methods of teaching reiki to the students.