The basic principle of homeopathy is “like cures like.” The idea is that something which, in large quantities, will produce a certain symptom, will relieve that symptom if given in a much smaller quantity. It’s a similar concept as vaccines — give a little bit of something to provoke the body to respond, without its having to combat the “full amount.”
Now here’s where it gets hairy. Most homeopathic medicines are so highly diluted there isn’t any of the actual substance left. That makes them very safe, but it also raises the question of, “how in the world could they work, then?” Nobody really knows. The presumption among most proponents is that the energy field or vibration of the original substance is still present even if the substance itself is not.
As you can probably imagine, the system is the subject of significant controversy. Some — especially strong proponents of allopathy — contend that it’s unscientific and has never been proven 1. Others — proponents of homeopathy, of course — contend that it has a sound scientific basis and hasn’t been studied enough to be proven or disproven 2.
I believe there’s room for open-minded skepticism. It’s true that we have no concrete explanation for how homeopathy might work. However, the fact that we can’t explain something doesn’t inherently make it untrue. Given its considerable safety, there doesn’t seem to be any inherent harm in trying it. (Avoiding the use of a different modality is a separate concern.)
I have not made much use of homeopathy myself, but my secondhand observations lead me to conclude that the most important factor in finding success with homeopathy is a knowledgeable practitioner. Unlike allopathic medicine, which matches drugs to symptoms, homeopathy primarily matches remedies to individuals (a concept unfathomable to many westerners). Consequently, skill in matching the remedy to the person is of particular importance.