Is it the soap or water that cleans your hands?

Yes to both: Water helps to mechanically and chemically remove dirt and water soluble substances. Soap dissolves fatty substances, oils, grease, etc. Soap helps destroy viruses, bacteria by messing with their cell walls; water is better than nothing. Alcohol based hand cleaners, e.g. Purell don't get rid off dirt, but can destroy viruses and bacteria-not spores though-not good enough for c. Diff diarrheas.