The expiration date (使用期限 Shiyōkigen) of a card refer to the last date that a card can be used, after which it cannot be used anymore. As of now, it is exclusively used on free cards and replaces the flavor text on the card.
Previously, free cards either comes with inferior stats or has a time limit on their abilities. The expiration date effectively replaces the time limit on ability, reducing the amount of text, but at the cost of rendering the card itself unusable. Expiration date is also unaffected by any other changes such as errata.