From Bulbapedia, the community-driven Pokémon encyclopedia.
A Wonder Card is sent together with a Mystery Gift, and it usually provides detail for the gift the player has received. In Pokémon Diamond, Pearl, Platinum, HeartGold, and SoulSilver, only three Wonder Cards can be stored at a time, and players must delete a Wonder Card in order to receive another one. This limit is raised to twelve in Pokémon Black and White. Discarded cards can never be retrieved.
Gifts bundled with Wonder Cards can be received from a deliveryman who waits in any Poké Mart. If a card is deleted before the gift is received in a Poké Mart, the gift will be deleted as well.
Obtained Wonder Cards can be viewed by accessing Mystery Gift on Pokémon Diamond, Pearl, Platinum, HeartGold, and SoulSilver's main menu (if it has already been unlocked), and selecting the "Check Card" option or the "Check the Card Album" option for Pokémon Black and White. Wonder Cards contain such information as the name of the bundled gift, whether or not the player has already received the gift before, the in-game event caused by the Pokémon, the date the gift was received in the game, and a brief description of the gift; an icon of the associated Pokémon is also displayed for further identification.
Some Wonder Cards may also be sent via DS Wireless Connection, enabling a player with an event to distribute the card for the event to players that do not yet have it.