To get past the authentication required message, you'll need to verify your account. This usually involves entering a special code sent to your phone or email, or answering some security questions. It's like a quick puzzle to solve before you can get back to gaming.
Google Play Store Asking For Authentication at Hiroko Hall blog
Once you've authenticated, you can go back to downloading that game you wanted. And if you're lucky, you might even discover some new game recommendations based on your playing history. The Google Play Store is always trying to help you find your next favorite game.
