A redemption card is essentially an IOU — you pull it from a pack, but instead of getting the actual card right away, you exchange the redemption with the manufacturer and receive the real card (usually an autograph) at a later date.
Modern redemption cards have a code printed on them that you submit online. Once processed, the manufacturer sends you the hit when it's ready. Redemptions exist because sometimes players haven't signed their cards by the time the product ships.
The waiting game can be frustrating — some redemptions take months to fulfill — but the upside is that you've locked in a premium card that's on its way. Just make sure to redeem promptly, as some have expiration windows.