Purified water is water that is completely free of radiation and as such can be safely consumed without harming the Lone Wanderer. In addition, it also heals far more than dirty water does. It's relatively rare in the wastes, but can be requested from Wadsworth or Godfrey inside My Megaton house or Tenpenny Tower suite respectively, at a maximum of 5 per week.
Each bottle of purified water appears to feature the text "'H²O" hand written on the label on the side of the bottle. This format is incorrect (at least according to IUPAC nomenclature) as in chemical formula numbers are written in subscript (Xy) and not in superscript (Xy). If read literally, the chemical formula H²O would mean there is one hydrogen and one oxygen isotope that contains two neutrons (instead of the standard eight). This would leave the oxygen extremely unstable and radioactive with a half life that would be so small that it would not be measurable.