Adding known email senders to the Gmail approved senders list allows recipients to avoid to have good email that might look like spam ending in spam / junk mail folder. Senders who have been added to the sender approved list bypass email filters.
For email marketers to work their way toward approved senders lists is a way to manage deliverability issues.
The approved sender term is used in particular by Google Gmail interface but the principle of approved senders lists is also used by other email clients and services under other names like safe senders list for instance.
How Clickz is seeking to become an approved sender in the email footer: