Public projects can be visible to all registered users on site. If projects not assign to user, still he can access it. Tasks of public projects also visible to all registered users on site. If user not assign to public project’s task still he can access it.

You can enable public project feature in miscellaneous setting. For this please go to Dashboard > Projects > Settings > miscellaneous. You can set this feature enable/disable. User can make project public while creating project. Also, admin user and project creator can set project privacy public/private in open project form.