You buy a kit that comes with a plush Elf toy and accompanying book. The idea is, the Elf lives in your house at Christmastime but each night when the kids go to bed, the Elf flies back to the North Pole (ostensibly to report back to Santa on the kids’ behavior which isn’t weird at all). Each morning, when the kids wake up, the Elf is back in the house. Here’s where it gets interesting (or tiresome depending on your view): the parents have to think up new and inventive positions in which to arrange the Elf each morning in order to keep the kids interested and make it believable that the Elf is actually alive and hanging about the house. There’s websites dedicated to giving parents ideas on it:
https://parade.com/living/elf-on-the-shelf-ideas