This is always an interesting question to answer for a homeopath as to truly understand the science behind how homeopathy works one must first feel comfortable with the concept of quantum physics, that "there is more to life than the eye can see", and with the term energy and energetic medicine.
Naturally people not adapt with these concepts or who hold a very simplistic and mechanistic view of the body and disease could find it quite difficult to comprehend and feel comfortable with how a medicine with this sphere of action can be so powerful and effective, but I will do my best to explain it in the way that I understand it.
The simple explanation is that homeopathy is a medicine based on two principals, the Principle of Similars; that a substance that produces symptoms in a healthy individual can be used to treat similar symptoms in a sick person, and the Principal of Minimum Dose; that one should only take the minimum amount of a substance required to initiate a response.
The medicines that we use to treat conditions are derived from plants, animals and minerals, but unlike naturopaths who would use the whole plant to stimulate and effect in the body, homeopaths administer these substances in there potentised form; a process which involves a series of dilutions and succussions (preformed at a homeopathic laboratory) to create the potency or strength required.
It is this potentisation process which gives homeopathic medicines the term 'energetic medicine' as there is no active molecules remaining in the newly formed substance, what is now created is the very potent energetic profile (if you like) of that substance. This medicine, with all of its know symptom picture, is then prescribed to an individual presenting with a similar symptom picture, with the intent to create an immune response stimulating the bodies ability to fight infection and susceptibility to disease.