Homeopathy is based on two fundamental ideas that skeptics like Singh can only shake their heads at. The first is the idea of the law of similars. The inventors of homeopathy believe that the cause of a symptom should also be treated with the cause. When treating someone, a homeopath considers which substance would cause the same symptoms in a healthy person. Arsenicum album, for example, which the activists in the campaign tried to overdose on, should in theory cause restlessness and nausea in a healthy person. But in an ill person, it is supposed to heal exactly these symptoms. If a patient has a fever, then a homeopath will look for a substance than can cause a fever in a healthy person.
The second principle is that of dilution: The more a medical ingredient is diluted and shaken, the stronger its effect will be -- at least that's the assumption. But most homeopathic substances are so strongly diluted that molecules of the active ingredient can no longer be traced. Homeopaths still believe in the effects because they are convinced the water has a "memory." Scientific proof for the claim is wanting.
Worth the read. According to the article, the dilutions used have gotta make you wonder: D23 is the equivalent of adding 1 drop of active ingredient to the Mediterranean; D78 is the equivalent of a few molecules in the entire universe, and apparently the homeohustlers make and sell preparations up to D1000. Shake well, indeed. Below: XKCD's acerbic viewpoint.