Very simply, the honey or semi-washed process is half-way between the washed and natural processes. Briefly, natural coffees are dried in their fruit (skin, pulp and mucilage all) while washed coffees are de-pulped and washed (with their skin, pulp and mucilage fully removed) before being dried. In the honey process however a certain amount of mucilage is left on the bean before it is dried.
These coffees often exhibit the best qualities of the washed and natural processes: clean and bright but still somewhat fruity and full-bodied. The best of both worlds!