A form of medicine practiced since its conception in the early 18th century.
In a nutshell it is based on effecting the organism through an infentismal amount of medicine. A homeopathic preparation can be dilluted down to a point where the original material - be it a derivative of a plant, animal, metal etc.. - no longer can be physically traced. All that is left is its imprint on the water it was dilluted in. The dillutions range from 1:10 to 1:1,000,000 (medicine:water). This form of medicine is a contravertial topic due to it using a 'vitalist' (vital/subtle energy) model in comparison to allopathic medicine's approach which builds on Germ Theory (a materialist approach).
Read more in-depth about Homeopathy at Wikipedia.
homöo-wiki (German)