Though with most open-source projects, the public is free to test whenever they feel like it. In this case alpha usually means it isn't really usable and that things are definitely not going to work right, if you want to use alpha software you are probably going to encounter problems with it. At the beta stage it is refined to the point where you could use it and get by with minor problems, and after beta is either the final release or a "release candidate", a build that is complete enough that if necessary would be able to be the final release, but a lot of times developers will use a release candidate for one last round of testing before the final product.
This was the case with Windows 7, the very early builds that leaked out on BitTorrent were pre-beta builds (somewhere between alpha and beta stage, it was complete enough for use but limited to developers, though after it leaked anyone could use it). Then they released a beta version to the public to test which was more complete and ran better, and eventually they released a release candidate that was very close to the final version but still had the ability to report last-minute feedback.