In a nut shell, an AutoSupport is a collection of data from Data ONTAP when certain events happen, when a customer triggers it or at the end of the week that is sent back to NetApp and is used to help us proactively support the customer.
There is a good write up on the benefits found in the document: http://media.netapp.com/documents/wp-7027.pdf
There is a wonderful customer perspective blog entry that was done years ago called "NetApp AutoSupport Rocks" describing the merits. The archive of this can be found in: http://www.vmunix.com/mark/blog/archives/2006/01/23/netapp-autosupport-rocks/