Elf on the shelf is a relatively new Christmas trend in the US. It is basically the combination of a book and toy elf designed to be a fun Christmas game. In th emonth leading up to Christmas, The elf on the shelf is supposed to watch over the home each day to see if the kids are being naughty or nice, then fly off to the north pole each night to give his daily report to Santa. Each morning he returns from the north pole and then "hides" in a new place watching over the home again, so it becomes a fun game for the kids to find where the elf might be hiding each day. One of the rules of the game is that children can't touch the elf otherwise it will lose it's magic.
I personally think this tradition is creepy for several reasons. Aside the eerie expression on the elf's face, the fact that he is supposedly watching and listening to everything and then reporting it to Santa seems like such a desperate way to keep children in line. Lets be honest do children need yet another lie at christmas? To make matters worse, if you child's friends don't have an elf in their home it gets very had to keep them believing in it, you then need to make up more lies to explain why their friend's home doesn't have an elf, and in that case how on earth can Santa know what's going on their home! It is also extra work for the parents to remember to move the elf into a new spot each night without letting the child see that the elf has been touched or moved manually.
Children should be good all year round as a matter of principle rather than because a creepy elf doll is spying on them and reporting back to Santa. It doesn't really send out a good message, it teaches them that they only have to be good when someone is watching and there is an imminent reward. This is one christmas tradition that really makes very little sense to me, hopefully it dies out soon!