Private Stories are just for you. Only you can add Snaps to your Private Story, and only you decide which friends can view it. Private Stories have a padlock icon.
Friends that can view your Private Story will see those Snaps mixed in with your My Story. On Android devices, Private Stories and My Stories may show up separately.
Friends that can't view your Private Story are not notified that you have one.
Remember that the Snapchatters who view your Private Story can always screenshot or screen record, so don't share content that you wouldn't want someone to save or share.