Homeopathy is a type of alternative medicine invented in the late 18th century by German physician Samuel Hahnemann. It is based on two ideas: "let like cure like" (similia similibus curentur), meaning a substance which causes disease symptoms can also cure those same symptoms; and that dilution with a large quantity of water increases potency. Both ideas are not only the opposite of what medical science usually observes, but the opposite of common sense too.
Homeopathy is fundamentally different from herbal medicine, with which it is often confused. While some "homeopathic" medicines are simply herbal supplements labeled as homeopathic, often to take advantage of regulatory loopholes, true homeopathic remedies are so greatly diluted they contain no active ingredients. The only measurable ingredients are the putative "inactive" ingredients, such as water, alcohol, or sugar. Those homeopathic pills for sale at your local pharmacy? They're sugar pills, prepared by taking a sugar pill, letting a drop of the homeopathic preparation fall on it, and then letting it evaporate away. What you're left with is the original sugar pill you've likely spent considerable money to obtain; and yet, this fraud is perfectly legal.
The scientific and medical consensus – based on numerous studies and meta-studies – is that homeopathy has no effect other than the placebo effect, which is not surprising considering homeopathic "medicine" typically contains no active ingredient. While evidence for the efficacy of conventional medicine was strong in placebo-controlled clinical trials, the evidence for homeopathy was weak and any efficacy was likely caused by the placebo effect. Aspects of homeopathic practice such as elaborate "provings" and one-on-one consultations can raise a patient's expectations and thus position homeopathy to be an especially convincing placebo – but still a placebo.