A blog post from Google announcing the new feature explains, "It's an extra step, but it's one that significantly improves the security of your Google Account because it requires the powerful combination of both something you know--your username and password--and something that only you should have--your phone. A hacker would need access to both of these factors to gain access to your account."
The feature will be rolled out to all Google accounts over the next few days. The initial set up will take about 15 minutes according to Google. Google has made the setup process more user-friendly, and has also expanded availability to more countries.