Autoresponders are useful to webmasters in a few ways:
They can be used at your technical support email address to tell your users that you have received their message and will get back to them soon. Such messages are important because it reassures your customers that their support request has arrived at its destination and will be attended to when you are available.
It can be used to send prospective customers information like the price list of your products, your FAQ (frequently asked questions) and other fixed information. People emailing that address will automatically get that message in reply.
It can be used to send email course modules. For example, if you have a three week course, with course information or documents to be sent to your students once a week, you can simply request your students to send their addresses to your autoresponder. The autoresponder will then reply to your students with the course package at the scheduled times.
A variation of the above is used by some webmasters to sell their courses. They advertise a particular address by which customers can receive a free sample of their courses (or book). The autoresponder then sends (say) 3 chapters from the course or book to the customers over three successive days. On the fourth day, the message asks the customer to sign up for the rest of the paid course or book if they wish to continue. Since the customer has sampled three segments (or chapters) of the course or book, he/she is able to decide whether or not to continue. If the course or book was particularly good, the autoresponder segments can be an effective sales gimmick to draw the customer to buy that product.