The Elf on the Shelf is a Christmas tradition based on the book The Elf on the Shelf: A Christmas Tradition by Carol Aebersold and her daughters. The tradition involves a Scout Elf who flies to the North Pole each night to report on the children's behavior and then returns to a new location in the house the next morning. 
Here's how the Elf on the Shelf tradition works:
Adopt an elf
Families buy a Scout Elf from a retail center and give it a name. 
Set up mischief
Each night, the elf's owner sets up a scene for the elf to get into. This could include spilling cereal, climbing the tree, or leaving footprints. 
Report to Santa
The elf flies back to the North Pole each night to tell Santa if the children have been good or bad. 
Return to a new location
The elf returns to a new location in the house each morning for the children to find. 
Encourage positive mind set
The elf can also suggest kindness activities for the family to do or leave positive messages.