Private teams can only be joined if the team owner adds you to them. They don't show up in search or your teams gallery.
Public teams are visible to everyone from the teams gallery and you can join them without getting approval from the team owner.
Make a public team private
To change the privacy settings for your team from public to private (or vice versa), go to the team name and click More options > Edit team. In the Edit team dialog box, under Privacy, select either Public or Private.
To change a team's privacy settings, go to the desktop or web app.