FollowMyHealth® uses something called Open Authentication as login for the site. This means that you can use your login from AppleID, Facebook, Google, Yahoo, or Microsoft LiveID to log in to FollowMyHealth, so that you do not have another username and password to remember.
The way the login through these sites works is like this: (let's use Google as the example) when you log into FollowMyHealth, the page that comes up requesting your username and password belongs to Google. You give Google your username and password, and they verify if it is correct or not. The first time you log in, a unique, randomly generated code is created to identify you. Once the username and password is verified by Google, that unique code is what is passed over to FollowMyHealth so the system knows what account to log you into.
Google knows that you (the user) have granted access to that unique ID to a third party site (in this case, FollowMyHealth), but once their login window closes, they do not have access to the content of the site or your activity there.
FMH Secure Login security info here.