Wrapping paper, or simply wrapping, was paper used to conceal the nature of a gift.
In 2266, James T. Kirk asked Helen Noel if she wanted him to "manufacture a lie, wrap it up as a Christmas present for you" (pretend to care about her). (TOS: "Dagger of the Mind")
In 2365, Data's slow unwrapping of a present was criticized by Wesley Crusher, who told him he was supposed to rip it off. Data assured him that if it was unwrapped carefully, it could be re-used, but Crusher felt the android had missed the point. (TNG: "The Measure Of A Man")