He's using standard software release terminology.
Stable is the current release that's recommended for wide use.
Beta is the next release. It's been through at least some testing, a few folks are using it, and things seem OK, but waiting for more testing and more feedback before declaring it stable.
Alpha is the release after beta. It hasn't had as much testing as Beta, so chances are higher that there's a bug or some sort of problem.
Generally you'll want to just use the stable release. You can use the beta or alpha, especially if one of the changes affects you, or you want to participate in testing and feedback. Just be aware that there could be problems with a beta or alpha release.