If you are an Android user, you definitely know what is Google Play :) (or you no need to be an Android user, you may know because it's really famous). Yes, Google Play or Google Play Store, and originally the Android Market, is a digital distribution platform operated by Google. It serves as the official app store for the Android operating system, allowing users to browse and download applications developed with the Android SDK and published through Google (wikipedia). You can download all the apps (free of charge or at a cost) from Google Play to your Android devices and use it immediately after installing. You also can sign in your Google account in web browser then choose the app you want, when your device is connected to internet, the app will automatically download to your devices. To sign in Google Play Store, you just simply enter your Google Account :) as I said in many old posts, one account, sign in all Google products. If you don't have an Google Account, you can sign up gmail - as well as Google account and start using other products.
Google Play was launched on March 6, 2012, with the merger of Android Market, Google Music, and Google eBookstore, marking a shift in Google's digital distribution strategy.
If you are not an Android user, means you don't have Android phones, tablet or smartphone, you still can play all the games from Google Play in your computer by installing Bluestacks or Andy - the emulators that allows you run Android app/game in your computer, full screen ;) It's easy and free.
To download these emulators, you can visit http://bluestacks.com or http://andyroid.net
After downloading and installing like other app in your computer, you will be aksed to sign in your Google Account like when you use an Android devices. Then you can start using like any other Android device with these emulators.