With Continuous Service enabled, you will be billed automatically at the end of your subscription's term at the market rate for your subscription. The renewal will be billed to the card originally used to make the purchase.
If that card has since expired or the account has closed, you will receive a renewal notification by email that will give you an opportunity to update your billing information.
Some subscriptions purchased from zinio.com have a Continuous Service option on by default. In some cases, Continuous Service is a default option that cannot be turned off during the initial purchase. In these cases, you will need to buy the subscription with Continuous Service ON, and turn it OFF afterwards.
If you don't see either options on an active subscription, that means continuous service is not an option for that title.