You're in control which job posts are visible on your career site. When you choose to post a job ‘open to public’ it’s accessible to applicants and visible on your career site. When you switch a job to ‘private’, it won’t show up on your career site. If you want to share a private job, you can still do this by sharing a a unique, private link.
Private job posts are most often used by companies who only want to share the job post within their own organisation. Also, most companies publish their job posts open to the public. When they have received enough applicants, they switch the job to ‘private’ and start reviewing and communicating with applicants. When they've hired someone, they finally ‘Close’ the job.