Homeopathy is a system of medicine based on The Law of Similars. This means that a remedy that causes a particular disease condition in a healthy person can aid the recovery of an unhealthy person suffering from that condition. It was formalized into a specific system of treatment by a German physician in the late eighteenth century. The underlying premise of homeopathy dates at least as far back as Hippocrates (same as in the "Hippocratic Oath" physicians take) in 400 BC.
It was part of the mainstream medical establishment in the U.S. until the development of the American Medical Association in the early 1900's. Homeopathy, like all of the alternative therapies, encourages your body to correct the underlying cause of the disease state rather than just suppress the clinical signs.
Homeopathic remedies are prepared in a manner almost completely backwards from common prescription drugs. The only similarities are the forms (liquid or pills) and the fact that none of the crude original substance is present in the final form. For instance, the standard regular drug for treating malaria comes from tree bark while a very high tech drug used to treat difficult skin infections starts out as ground up bug bodies. (This would be a good time to look up the dictionary definition of "antibiotic" listed in the "Glossary" section.) But you won't see bits of branches in the syringe the doctor uses for your malaria. You also won't even so much as see the yellow color from the sulfur a homeopathic doctor might use for your skin condition.
The difference appears in how the natural form is transformed into the final product. Megamillion dollar drug companies spend years isolating the one chemical in the natural product that is assumed to be responsible for its beneficial effects. Then they concentrate it a thousand times or more. Finally, they put it through a series of cell culture, computer, and live animal tests to determine the best dosage amount and frequency. If the benefits outweigh the side effects, or if there is enough urgency for the treatment, of it there is enough pressure for approval, the FDA allows the new drug into the commercial market.
Because of the way homeopathic remedies are prepared, the less of the original substance that is in the final mixture, the more potent that remedy becomes. Most of the remedies are prepared in either "X" or "C" potencies. When you place one drop of the original substance (called a "mother tincture") in nine drops of a diluting liquid, you can create an "X" potency. One drop of mother tincture in ninety-nine drops of dilutent creates a "C" potency. These steps are repeated for a series of dilutions. Any toxicity found in the original substance disappears after three 1:9 serial dilutions (3x). At the level of 6X (six sequential "X" type dilutions) there is only 1/1,000,000 (one millionth) of the original substance in the remedy.