does an elf on the shelf really move

Indeed they do! The elf on the shelf is a special kind of elf that is known for moving around and interacting with the children it watches over. They are magical and mysterious beings that can travel to and from the North Pole, and they have the power to make sure the children are behaving themselves. But they also have a sense of humor, and they love playing pranks and jokes on the children they watch over. So yes, an elf on the shelf can certainly move and cause a lot of mischief!