I can't seem to find an explanation or detail on what happens, what is synchronized, if, when you use Trello with a Gmail or Google account? Can you synch the Task list? Calendars? Emails? Where does it live? What does it look like?
Google is just the OpenID provider. Jeff Atwood explains OpenID rather well in this blog post:
There is no synchronization. You use your Gmail/Google-account to login on Trello. So instead of using/creating a new login on yet-another-webservice you re-use your previous account.
We're trying to get your profile picture from Google, at some point in the future, too. Right now, people have to create an account at gravatar.org to get one.