While some homeopathic remedies may have some as yet unproven benefits, such as mind over matter, the basic scientific assumption is that many of them lack credibility. Homeopathy is basically the legal marketing of quack products for drugs or for their purported medicinal benefits. These drugs are supposed to cure by reviving the body's "vital force", whatever that is.
Water often plays a vital role because many of these products are made from minerals, botanical substances, or several other substances that are diluted to extremely low concentrations in distilled water. The water serves as a carrier for the drug. Some of the dilutions of these products are so extreme that it is unlikely that even one molecule of the original product can be found in the distilled water. It is claimed that these products make an imprint on the water molecules, and that allows the water itself to carry the healing power of the original drug, even though its presence is no longer perceptible.
The most characteristic and controversial principle of homeopathy is that the potency of a remedy can be enhanced by dilution, in a procedure known as 'dynamization' or 'potentization'. Life has evolved around water, into water, because of water: special water properties permit hydrophobic interaction, very few water molecules go with biological compounds keeping their 'imprint', water clusters 'activated' during homeopathic dynamization can reach a cellular receptor and trigger specific responses.
In homeopathic medicine, it refers to the making of a homeopathic remedy. This occurs by taking a substance - the original material in its natural state - and 'potentizing' it through a process of dilution and shaking (succussion). A substance is repeatedly diluted in water or alcohol in the ratio of 1:100 parts, and at each stage, the dilution is shaken vigorously, either by hand or machine. This mechanism of shaking changes the process from being merely a dilution to being an energetic, "vibrational" enhancement. It is a method of liberating the "essence" of a substance from its material form. The underlying concept that has to be recognized is that all things have an energetic vibration to them and potentization is a process of liberating and refining this essence.
The basis of all holistic thinking, whether it applies to Medicine, Ecology, Anthropology, Philosophy, Pure Science, or any other system of thinking, is that all things are connected. Whether we call it "Chi", "Prana" or "Vital Force", or any other word to describe the threads of energy that connect all things together, it is this energetic phenomenon that is the connecting principle.
Obviously, one must err on the side of caution when approaching homeopathic cures their combination with artificially enhanced waters of any kind.