It is a service they offer to renew your domain on an annual basis, even if you have a multi-year registration.
You register a domain name on July 2nd 2012 for 5 years. Your domain expiration date would be July 2nd 2017.
With regular auto renew, your domain would renew on July 2nd 2017 for another 5 years.
With extended auto renew, your domain name would renew after one year, on July 2nd 2013 and would be extended by one year (making the expiraton 2018, instead of the 2017 expiration you had when you originally registered it).
More info directly from GoDaddy:
What is Extended Auto-Renew?
Having a multi-year registration tells your website’s visitors that you plan to be a trusted, well-established online presence.
Extended Auto-Renew automatically renews your domain names each year to maintain their original registration lengths and prevent expiration. For example, if you select a registration length of five years for a domain name with Extended Auto-Renew, we automatically process a renewal each year to keep its expiration date five years in the future.
NOTE: Some domain name extensions do not allow this option.
If you set your domain names to auto-renew, we attempt to renew them and bill your credit card if the renewal is successful. If our billing attempt is unsuccessful, we send you three email messages asking you to update your payment information.
This features seems slightly pointless to me, but I suppose it could be helpful if you want to make sure you never even get close to an expiration date for a domain. It definitely accomplishes one thing: getting more frequent payments for GoDaddy