Apparently they provide natural pain relief for teething because "the skin warms the amber beads, releasing healing oils which are then absorbed into the bloodstream." Hmmm.
This website, among others, explained all about it but I gave up reading not much further on. It all sounded too much like Bad Science to me. I actually thought the skin was supposed to be a protective organ which stopped foreign things entering the bloodstream....
However, if anyone would care to provide some good evidence that they do work (not just anecdotes) then I would be happy to stand corrected. I read a few reports on parenting sites from parents who had put them on their babies well before they even started teething and then said stuff like "aren't these necklaces great, my baby didn't complain at all when he was teething." But that's not proof. Their baby might just have been a non-complaining teether anyway, like all my kids have been.
(Edited to add....I just deleted a comment because I was spammed by a website that sells them!!)