Then you would have to manually send emails to everyone on your list at regular intervals. What if your list totaled 10,000 email addresses? How long would that take you? Quite frankly, you couldn't do it. That's where the autoresponder comes in. Your opt-in form would be designed by the autoresponder. It would retain the details in its database, and automatically send the thank you letter to those filling in the form, together with any gifts offered for the address.
If you had offered a seven part course on, say, sheep shearing, you would write out the seven parts and then program the autoresponder to send out an email to new people at regular intervals determined by yourself. You can program them for once a day or once a week. Some autoresponders can send them once an hour.
If somebody purchased your product, the autoresponder would send a thank you email, and then transfer the name and email address to a different list. This makes sure that, if you send out regular emails promoting a product, then somebody who purchased it would not be sent the same emails. They would be on a different list.
The autoresponder can also send out many emails at predetermined times to each list that you have separately, so that all do not receive the same email. Could you send out an email every two weeks or so to ten thousand people? If somebody makes a purchase, they are sent their product, if it is electronically deliverable, receive a thank you letter and are even contacted to make sure that the product is doing what it should. During all this you could be sunning yourself on the beach.
They can also operate your double opt-in system, sending an email informing the visitor that has just completed your opt-in form that there is a confirmation email in their inbox awaiting them, accept the double opt-in and transfer the email address to the list of your choice. In fact an autoresponder can be set to run your business, and all you have to do is go to the bank and check up on your ever increasing balance.
The only thing wrong with the importance of autoresponders in internet marketing is that they are wrongly named. They are not autoresponders. They can send emails when they are triggered to do so, but they cannot respond to your emails. Try sending a reply to one and see what happens!