1. What it is: It's an extra layer of security for your online accounts.
2. How it works: For both Google & Dropbox it works like this, you enable it on your account and when you sign into a new computer or a device you must enter your password as well as code that they have sent to your mobile phone.
3. Why you should care: By asking for a code from your mobile phone (you set up what number they use when you enable the verification) it means that a hacker can't just obtain your password and get into your account, they must also have access to your mobile phone.
4. Does this make me 100% safe? No, nothing does, but it does make your account much, much more secure and had this been enabled on my Google account, it and the others that were connected to it, would not have been hacked.
Have you enabled two-step verification? If not, why not?