The Development Status of software defines how mature the software is.
Alpha indicates that the code is very likely to be highly unstable, and is not recommended for use in a production environment. Alpha software typically isn't anywhere near feature complete, and severe limitations may be encountered during use.
Beta indicates one of many things, depending on where in the software world you are. Smaller developers may tag a build as Beta if they feel it is reasonably stable, and mostly feature-complete. However, many developers may wait until their software product is feature-complete, and then use the Beta development phase to iron out existing bugs, test server stability, and run simulations in preparation for a full release.
Seen in both open-source and closed-source software, a Release Candidate is a statement from the company that says "We believe that this product is ready for an official release, however, additional testing is required to confirm this".
Speaks for itself.