When you start development on Xamarin targeting Android, chances are you need to test it on an emulator. So comes Android Player. It is a pretty cool emulator where it gives you a better interface to create target test emulator and configure a bunch of other stuffs like battery and gps.
Besides downloading and installing Xamarin Android player. You also need to setup Google Play services on this emulator.
You can obtain Google Play services for different Android version from here.
Download and drag it in to the emulator. Once restarted, you're good to go and it will install whatever updates required to bring your emulator current.