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Double Authentication is an another security layer to help yourselve from the hackers. More over this service is directly provided from your Google account so we can know how secured the login will be. Google also provide you some backup codes to print on any paper, this is because when your unable to access your mobile we can go through this backup codes entering whenever code/pass asked. Google also provided Google Authenticator for Android users so they never require to request a new code always, a temporary code will be generated which will last for 20-60 seconds. In that given time you can use the code to login.
Thanks for providing the wonderful plugin.
I had included this plugin on my blog with how it works.

[ Moderator note: Link removed. When your site insists on an email before you can view your post then that is spamming. That's not allowed here. ]