Homeopathy is often used as a blanket term for any kind of alternative or herbal medicine, but it is actually a very specific form of medicine based on the Law of Similars, or the idea that ‘like cure likes,’ developed by Samuel Hahnemann of Germany in the 18th century. A remedy, given in infinitesimal doses, is chosen based on the totality of the symptoms affecting the patient, both physical and mental. For example Coffea Cruda is a remedy made from coffee. While coffee itself can cause nervousness, over-sensitivity, racing thoughts, palpitations and restlessness in people, the remedy can be used to cure people of these very same symptoms and is often prescribed for those suffering from insomnia. 

For a more in-depth explanation of homeopathy and its basic principles, this page has the best explanation that I have found: What is Homeopathy from Whole Health Now 

For even more information, here is a whole book about homeopathy that you can download for free: Homeopathy: Beyond Flat Earth Medicine by Timothy R. Dooley, N.D., M.D. 

This is the book that started me on my own journey with homeopathy. It is written by a woman that successfully used homeopathy to recover her son from autism. Impossible Cure: The Promise of Homeopathy by Amy Lanksy