Double opt-in (usually) refers to an e-mail mailing list subscription confirmation system where a(ny) person requests subscription to a mailing list, providing an e-mail address and, to that address, is then sent a subscription confirmation request, usually either providing a unique URL, a URL with login name and password or an e-mail reply request to confirm the subscription before the e-mail address is added to the list as a valid subscriber.
Double opt-in systems are used to prevent unauthorized subscription of people to mailing lists without their permission and are blatantly ignored by unsolicited bulk e-mail senders around the world.