While studying allergies in 1984, Jacques Benveniste, M.D., research director at the French National institute for Medical Research, observed that when highly diluted solutions, or homeopathic remedies, were administered to allergy systems, the systems reacted as if molecules from the active ingredients were, in fact, still present; in other words, it appeared as if water retained some trace of the active molecules. This controversial theory has since become known as "the memory of water."
Source: Nature, 1988, vol. 333.