What does alpha test, beta test, and production mean in the Google Play Developer Console?

There is not much difference between tests alpha and beta except that you start with a small group for alpha testing and move on to a larger group for beta testing.

Production is the term that is used when your app is available to your end users, the ones for whom you made the app (that is, when it is available for anyone to download or purchase from the Play Store).

For alpha and beta testing you need to send invitations to those interested in your Google+ accounts so that they can access and download your application. Invitations usually take the form of a link directing them to your app in the Play Store, which is only visible to them when they have accepted the invitation.

From the Google Developer Console :

  

How do I get started?

     

We recommend starting with a small group of   Alfa testers, and then expand your test to a group of   Beta testing.

     

Should I use open or closed Beta testing?

     

Closed Beta: use this   option if you want to run a test with a smaller group (as in your   company or team) or when you know exactly which users   want to test your app. If you test an already published app, only the   users in your test group will receive a version upgrade   Alpha / Beta.

     

Open beta: use this option if you want to test with a group   and view the Beta version of your app in the Play Store. If you   to perform an open beta test, anyone can participate in the   your Beta program and send private comments to you. Check   if the app is ready to be visible in the Play Store before   choose this option.

     

The open and closed Beta versions of your app will not have appraisals   public.