Published sites are available to all site participants and appear in their site tabs and lists.
If the site is left as draft, or unpublished, only instructors/site owners may access it and students will not see the site in their list of sites. Throughout the site, instructors will see the Unpublished Site banner and can use the Publish Now button to quickly publish a site, without going through Site Info.
If site visibility is set to Display in Site Browser, all people with access to the Sakai system may search for the site from the Worksite Setup tool. If set to Do not display in Site Browser, the site will not show up in a search.
In most cases, site owners keep the default value Limit to official course members or to those I add manually (recommended). This will restrict enrollment to people that you add manually or that are enrolled automatically from the registration system.
If the site is set to Display in Site Browser (as shown above) AND the option Allow any Sakai user to join the site is selected, anyone in the system may search for and join your site.