The 'Private Gallery' is only viewable by you, this means no other members can view any photos uploaded to your 'Private Gallery'.
When on the app, if you view your own profile, you will see your Private gallery, but this is only viewable by you!
The 'Hidden Gallery' can be used to store photos you don't want to be visible to every member.
You can attach photos from your 'Private Gallery' to your messages with other members.
Should you wish to remove the attached photo from a message, you would need to remove the photo from the gallery as it's linked to that message, and re-upload the image again to your 'Private Gallery'.
All other galleries are visible to Premium members but only the Main Profile gallery is visible by standard members.