You may have used two-step authentication recently, as tech companies look to beef up security. Usually, you get a code texted to you, or whatever, and it is a bit irritating and fiddly.
You get a fresh six digit code (or more), and it enables you to log-in to your account or app, and it has been annoying a whole load of people.
Google have noticed this, and want to make the whole process smoother, and less jarring. Basically, it'll be faster, and it'll soon be available for both Android and iOS.
To use it on your iPhone, you'll need the Google Search app installed.
Basically, instead of messing around with codes, when you log into a Google account (or another service that needs you to use your Google credentials), you'll be sent a notification asking if you're trying to log-in.
Instead of getting a code, you'll just tap the 'yes' button.
Of course, if you've turned off two-step notifications, this won't affect you. Should you want to, you'll have to turn it on (and you'll have to turn this on even if you are already using it).
As passwords are gradually being phased out by tech companies, this is something you're going to have to deal with, with more frequency.
How To Turn On Google's Two Step Authentification
Log-in to Google. Go to My Account. Hit 'Sign-in & security'. Sign-in to Google and hit '2-step Verification'.
That's also the place where you can turn it off, if you're not happy with the whole experience.