Public projects are visible to everyone. They show up in Transifex's Explore page and get indexed by Google. And non-Transifex users can see the public pages for a public project. That said, you still have control over who can translate your content and what user role each person involved in your project plays.
If you're crowdsourcing translations, we recommend making your project public. It's extremely easy to bring translators since they can find your project and request to join a translation team.
Private projects are only visible to the people who were invited to work on them. They won't appear in the Explore page, and Google will not index any of your pages. This is the recommended route if you have proprietary content that you don't want everyone to see. When your project is private, you'll need to manually invite people to work on the project.