This feature basically adds an account to your system (in this case a Gmail Account). It is the equivalent of opening System Preferences > Mail, Contacts & Calendars and adding said account there.
(On the screenshot I have only one account added: iCloud, but you can add as many as you want, from whichever services listed. Also note, I'm using Mountain Lion, which added support for more sites like Twitter and Vimeo).
Safari offers to auto add your accounts whenever you sign in for the first time, as I'm guessing many users don't know this preference pane is available.
Basically what adding an account will do is allow you to sync your information to the apps on your Mac. In this case, your Gmail emails would be downloaded automatically by Mail, your Google Calendar would be synced to iCal and you will be able to use Google Talk with iChat, if so you choose.
If you click "no" on the dialog box, it wont re-appear (as to not annoy users every time they want to log in) but there is nothing special about the dialog itself, it just saves you opening System Preferences and adding the accounts yourself.
Hope it helps!