You've basically got it. A private beta is designed to test if you have all the moving parts needed to have a successful launch on opening day. We don't create sites based on "If you build it, they will come." It all has to come together with what you have right here. You've got to have enough content, people, interest, expertise, and governance in place before you can open to the public. See
Your New Site — Asking the First Questions
We don't have a lot of hard numbers to "pass" or "fail" a private beta — It's not a numbers game, and communities vary greatly — but what we do have is a lot of hard-earned experience comparing your content and the activity with the patterns of success and failures of sites that came before you.
So here are the type of issues we look at during the private beta. This is by no means comprehensive:
Do the questions define a well-focused and comprehensive site? Does the subject form a coherent community which isn't already better served elsewhere? Are questions real, expert questions which would be asked by actual practitioners in the subject? Will those questions be interesting to an expert audience?
Audience & Expertise
Do we have the right audience founding the site? Was there enough sustained interest in the site once it launched? Are they asking real questions and providing expert answers? Is the vetting of questions and answers sound — i.e. are they quick to correct mistakes, voting to push the best answers to the top, commenting to improve the content, continually posting better answers where they can be improved, etc?
Is there enough interest in helping administer the site and helping it grow? Is the site developing a core community of leadership? Is there enough participation and voting to create a core community of avid users who will edit/close/moderate, etc? Are they adopting a Stack Exchange philosophy and interested in teaching others the proper use of the site? Are the participants generally cooperative and resolving issues of scope, content, and site administration?
Does the subject scope add to the network or just duplicate content found elsewhere? Are they likely to create a relevant resource in their subject space? Are there better solutions to their problems on the Internet, in general? Is the the subject and participants likely to make the Internet better overall?
In other words, will this site likely forward our goal of "making the Internet a better place to get expert answers to your questions?"