Although it hasn’t been made official yet, according to this Engadget early report, Google is playing around with an idea of allowing its users to log into various Google accounts without having to use a password once a mobile phone has been verified using 2-factor authentication. Once your phone is authorised, in order to be able to log into a Google account from your PC or laptop, all you have to do is, place your phone near the computer. For example, if you need to log into your Gmail account, go to Gmail.com, the system sends a message to your phone using GCM (Google Cloud Messaging) which pops up a notification for you to allow the connection. As soon as you tap on the confirmation on your phone, you are logged into your Gmail account.
What if your mobile phone is not around? Then you can use the old way of entering your username and password.
Here is the link to the Reddit user who has been trying it this new feature. On this link the user also links to a few pictures that he/she has posted.