It is the second most popular system of medicine in the world; used by hundreds of millions of people. It's a safe, effective, holistic form of medicine without toxic side effects. Some of its fundamental principles include:
Treating the whole person. In other words, you will receive a remedy that is personal to you and all the unique symptoms you express physically, mentally and emotionally; rather than solely to your diagnosis.
The principle of Like cures Like. That is, the understanding that substances that can cause particular symptoms in a healthy individual, can be given in highly diluted form to cure those same symptoms in diseased individuals. For example; onions, which can cause watery eyes and a runny nose, can be used as a remedy (called Allium cepa) for hay fever.
The Society of Homeopaths also have an article - for more about what homeopathy is.