The response or reply card is included with the wedding invitation, along with a printed stamped and addressed envelope, and asks the recipient to respond to the host as to whether or not they will attend the event.
The recipient(s) writes in the name(s) of all who have been invited, indicates whether or not they plan on attending by checking “accepts” or “regrets”, places the card in the provided envelope, and pops it in the mail.
Once upon a time, the recipient of a formal wedding invitation would be expected to reply by sending a formal, handwritten letter to the host. Although, still correct but highly unlikely to happen in our modern world, a response card is the next best thing.
The names on the response card inner and outer envelopes indicate who has been invited.