In a nut shell, an auto responder is a way of sending an email out to a subscriber automatically when they do "something".
Usually this would be an email that is sent out to your user as soon as they signup, or maybe a couple of days later, or maybe both.
A good example might be an Ecommerce website. A customer orders something and opts to signup to receive newsletters. That moment an email is automatically sent to the customer saying thanks for their order.
A few days later another email might be sent out saying "How did you find our customer service", and then even further down the line another email might be sent saying, "Don't forget about us" if the customer hasn't used the site for a while.
You might even schedule an auto-responder to send emails to your customers wishing them a happy birthday.