Just like with the iPhone and iPad, Apple provides a way for developers to send ad-hoc versions of Mac App Store apps out for beta testing purposes. Since there are many apps out now that have iPhone and/or iPad versions as well as Mac versions, you might need to know how to install the Mac App Store beta version, and its provisioning profile as well. As long as you gave the developer the proper hardware UUID for your Mac, the process is fairly simple, and not dissimilar from the process of installing iOS beta software on your iPhone, iPod touch, or iPad.
That's it. If you have any trouble -- it's a beta app, after all -- check with the developer. You made need to trash some other, previously installed files, or do some other configuration first. When you do have it working, enjoy.
The Mac App Store isn't the only way to distribute software on OS X, so many developers may never need to send UUID-locked beta builds. But if the Mac App Store is the only way the developer intends to distribute their software, this may well be the beta road they take.