Homeopathy is a system of alternative medicine whose practitioners believe that if a large dose of a particular substance causes a symptom when administered, then the same substance would cure ailments causing similar symptoms when a smaller, more diluted dose is administered; this is called "like cures like". Practitioners repeatedly dilute substances with water and/or alcohol and vigorously shake the resulting solution; the resulting "remedy" often contains very little, if any, molecules of the original substance. However, homeopathists believe that this procedure makes their remedies more potent through a phenomenon known as dynamization.
Homeopathy regards diseases as 'morbid derangements of the organism', that involve some disturbance in a 'vital force.' Today, most homeopaths still believe that the fundamental causes of disease are internal and constitutional and that it is contrary to good health to suppress symptoms. They also accept the concept of 'latent Psora', the early signs of an organism’s imbalance which indicate that treatment is needed.
Modern scientific consensus states that homeopathy is pseudoscientific; there is a lack of evidence to suggest that homeopathy's effects are any more than placebo,  and the basic premises of homeopathy seem impossible under our current understanding of the world.
Homeopathy was created in the 18th century by physician Samuel Hahnemann, who noticed cinchona bark, used to cure malaria, could cause malaria-like symptoms. He believed that his new system was more humane and effective than the conventional medicine of his time, but it was greeted by the establishment with derision and contempt. Since then, homeopathy became more popular. Homeopathic hospitals of the time were better for their patients than conventional hospitals, as they generally prescribed medicines that had no effects at all, while contemporary conventional hospitals had dangerous, potentially fatal treatments. As new medical discoveries were made and conditions in conventional hospitals improved, however, homeopathy fell into decline. Today, homeopathy is not an accepted part of conventional medicine, and its theories are not generally regarded as scientifically credible, but nevertheless it has more than 100,000 practitioners worldwide, and 500 million users.
All homeopathic remedies are created through repeated dilution of a substance.Remedies made with a soluble substance are made by diluting the substance with water and/or alcohol and vigorously shaking it. The resulting solution is then repeated diluted with the same process until the desired dilution is reached. On the other hand, when a homeopath uses a non-soluble substance to make a remedy, he would grind the substance and dilute it with lactose. The number of times a substance is diluted by 10 times its volume is marked with the number and X, while the number of times it is diluted by 100 times its volume is written as the number and C. In a 5X remedy, for instance, the substance would have been diluted so the solution has one part of the substance per 10^5 parts of the solvent. Most remedies are of a dilution between 6X to 30X.
Homeopaths conduct "provings" to find new substances with which they would make new remedies. In a proving, participants are given a particular substance without being told of what it is, and are asked to report on what effects the substance had on their bodies. The data collected from the proving would then, theoretically, allow the homeopath to understand what illnesses a remedy made from the substance would cure; such a remedy would supposedly cure illnesses with symptoms similar to those caused by the substance itself.
Homeopathy has many implausible aspects which do not make sense under our current understanding of physics and medicine. The high dilutions used in many remedies preclude them from having any effect on the body; a remedy with a dilution of 24X or above is highly unlikely to contain a single molecule of the original substance it's made out of, while common homeopathic remedies can have a dilution number of up to 30X.  Homeopathy's core teaching that the potency of a drug increases with dilution goes against current medical understanding, which states that, in most cases, the potency of a drug increases as dosage goes up, not down.
In order to explain away the fact that homeopathy is physically implausible, homeopaths hold that water has an ability to receive an imprint of the chemicals it had interacted with, and that it therefore would be able to retain the pharmacological effects of a substance, even if it had been diluted to the point that it's no longer existent in the final remedy. This concept is called water memory, and water having memory was first claimed to have been observed in 1988 by a French scientist only to be debunked two months later.
Many scientific studies have shown homeopathy to be ineffective; there is no sound evidence to suggest that its effects are any more than a placebo.  Although some studies and meta-studies do show some results that are promising to homeopathy, they are usually contradicted by later studies. For instance, a 1997 study concluded that homeopathy's effects are not completely due to the placebo effect, but still said that there was no evidence to conclusively show that homeopathy has much efficacy in treating any ailment.  The 1997 study was later contradicted by a 2005 study, which concluded that homeopathy cannot treat any condition whatsoever, and that its purported ability to cure illness was a product of the placebo effect. 
Homeopathic products are not as regulated as conventional medicine products; they do not come under as much scrutiny for their effectiveness. In the United States, the Food and Drug Administration regulates homeopathic products, but does not check for their effectiveness in treating illnesses or for their safety. While some states do require practicing homeopaths to be licensed, others allow homeopaths to operate without licenses. 
When homeopathic remedies, which are generally ineffective, are used to treat a serious condition, such usage could worsen the condition as it would delay treatment with proven conventional treatments. The National Centre for Complementary and Integrative Health has expressed concern over the use of homeopathy in lieu of actually working remedies, advising people to “not use homeopathy as a replacement for proven conventional care.”
In addition to that, some homeopathic remedies are not diluted enough to render its active ingredient or ingredients inactive; this makes it possible for them to cause real side effects, because they contain actual pharmacologically active ingredients.
Relation to liberalism
The connection between the usage of homeopathic remedies and liberalism is not proven nor discussed by any reliable source, but liberals have been shown to be more likely to believe in other pseudosciences than conservatives; for instance, more liberals believe in the pseudoscientific myth of astrology than conservatives.
Health food stores frequented by liberals may have homeopathic remedies in stock. 
David Copeland, a practicing homeopath and politician who passed legislation that exempted homeopathic remedies from certain forms of governmental scrutiny over their safety and effectiveness, was a democrat. 
- Hahnemann S (1796) translated into English as "Essay on a New Principle". Hahnemann's Organon der Heilkunst in English translation
- Dean ME (2001) Homeopathy and the progress of science Hist Scixxxix
- "British Medical Journal", BMJ 1 (533): 283–4, 1871 Registration required for access