Alpha is where programming for the software is still heavily ongoing. If you can start up the program without it rebooting the computer you're generally happy.
Beta is where you've gotten a great bulk of the program working (sort of) and you're letting other people try it out to test if they can use it or crash it.
Gamma is also sometimes called being "Gone Gold". It's publically (or commercially) released software. If it's in a box or shrink-wrap it's Gamma (you hope).
Omega is the absolute final release. Not all software publishers do this, but it is when they decide they're never going to work on the software again and generally release the entire thing for free, sometimes with the full source code.