We all hate passwords, between not being able to remember them and needing to change them all the time, it can really be a hassle. Not to mention the fact that passwords can get hacked, and do get hacked quite often. It's a good idea to change your passwords often, but many people don't. Google is looking for a way to keep our accounts safe but allow us to login to our accounts without needing to use a password. And if this user from Reddit is to be believed, it appears Google is now sending out invites for a way to sign into your Google account without a password. How awesome would that be?
Basically what is happening here is you are signing into your account on a desktop or another machine, but approving it from your phone. This is great in a couple of ways, one being that if someone tries to access your account and you don't know about it, you'll get a pop up instantly. In which you can deny the user access to your account (which you should definitely do). The other is that you can grant your computer access to your Google account without doing anything extra really, just allowing it from a pop up on your phone. Google notes in this email that they may ask you to prove your identity if they notice something sketchy about the login (like the location, IP address, etc), just to be sure it's you and adding a bit more security to your account.
We're unsure of how many people are being invited to this program, and even how users are able to be invited. But it is quite clear that this is beta, maybe even alpha. And Google does have a Google Group there for users that have been invited, so they can talk with each other about issues they may have, or even find out if the feature is worth rolling out to everyone else. Hopefully this is something we'll see rolling out to other users in the near future, but as for now it's just for a handful of users.