OK, I did a little research. The Medallion program is used onboard and in port. I'm not sure how it works, but it seems that it contains all the information that's normally included on the ship's card. If you're on a Medallion cruise, you can go to Guest Services and request a card.
The Medallion is just a disc that you can put in various holders. Necklace, bracelet, just a holder (sort of like a card).
I'm not sure I will like it, if I'm ever on a Medallion cruise. They did have issues when first introduced, due to the proximity sensors. I've read where random room doors were being unlocked when someone with a Medallion walked by (not their rooms). But, I think that's been fixed.
I find it a bit off-putting that, by just walking into a bar/lounge the bartender knows you're there and what you drink.