Auto-Responders are commonly used for the following:
Vacation Messages: Notifying anyone that sends an email to you that you currently out of office. For example - "I am currently out of the office and have limited access to Email. I will be back on Friday, 5th Oct. In case of any urgent work, you may contact Mr. Jack Sparrow at (144)-123-1961 in my absence."
Delivery Confirmations: Notifying anyone that sends an email that their message has been received. For example, an auto-responder for a sales email account - "Thank you for your Email. This is to confirm that your message has been received by us. We will be replying to you shortly."