To moisturize is to add moisture to something or make it less dry. The purpose of hand lotion is to moisturize your dry hands.
Moisturize is most often used to talk about beauty products, like lotions and moisturizers. If your skin's dry, oil or cream will bring some moisture and softness back to it. And, if your hair is brittle, conditioner will moisturize it and make it smoother. A diet with plenty of healthful fat can help moisturize your hair and skin too. Moisturize adds -ize, a verb-forming suffix, to moisture, from the Old French moistour, "dampness."