When I see an proposal saying "private beta" but I can go into it, what is a "private beta"? I think it is just saying the owner can visit, but I can visit the site.
The private beta is when proposal supporters can finally start asking and answering questions in preparation for a broader, public launch. The primary purpose of a limited-time private beta is to get head start on discussing the basic scope and administration of the site in preparation for opening day. The private beta also has reduced reputation requirements to help bootstrap the community to use many of the feature needed to administer the site.
Anyone can join the private beta. The private beta wall you passed through was there to inform incoming users that we are still in the early, formative stages of community-building, and that many of the most basic definitions and rules for the site are still very much in flux.
The private beta typically lasts about three weeks.