2 Step Authentication in Google is a way to increase the security of your data. Basically, 2 step authentication means that you have to provide your password and something else. Normally, that is a code from a device that you have (usually your phone). A code is sent to your phone each time that you log into a new computer. Google has just made a change so that instead of entering a code, you can now just confirm that new computer using your phone.
This makes using 2 step authentication even easier. 2 step authentication makes it much harder for hackers to access your data.