From Nookipedia, the Animal Crossing wiki
Wrapping Paper is an item in Animal Crossing: New Leaf that can be purchased from the Nookling Stores. It allows the player to wrap an item to look like a present. Wrapped items can be given as gifts (useful for when a villager celebrates their birthday) or mailed with letters. When placed in a house, wrapped items fall on the floor instead of turning into furniture. They count towards trash when being graded by the Happy Home Academy.