Your Tesco Clubcard, your Nectar card, every other plastic loyalty card or store card in your wallet, they all started life as plain plastic cards.
Most loyalty cards are just basic plastic cards with a barcode printed on. The barcode will have a unique number that can be registered by a barcode scanner, therefore accessing your account and adding points, benefits etc, although some shops, like Tesco, have moved across to contactless loyalty cards.
Using plastic for loyalty cards as opposed to paper or card means they last better when being kept in purses or wallets and can also have more detailed printing on them, feeling and looking higher quality and more premium.