Also known as verified opt-in or sometimes double opt-in, confirmed opt-in means that a recipient (your subscriber) has verifiably confirmed permission for the address to be included on your specific mailing list. By confirming (clicking the link in this message) a subscriber has given you expressed permission to send messages to their address.
For example, a visitor to your website enters their email address into a sign up form. The visitor is sent an email with a unique and personalized link, this is generated as soon as they sign up. The potential subscriber must click on that unique link in the confirmation message to verify their subscription to your list. This verifies the owner of the email address attempting to be subscribed is indeed the person that typed it into the website form.
For more information, please reference the Spamhaus project.