What is a non-public image?

A non public image is an image that is not visible in your gallery. Only the image owner can view the image when logged in to his account.

Why is my non-public image showing up in my profile page?

If an image lives in a subgallery of a non-public gallery, but the subgallery is not non-public, then the image itself is public and can appear in the random images on the profile page. You can easily check which of your galleries are public/non-public and which are password-protected by going to your root gallery and clicking the "tree view" link at the top right of the page. This will list all of your galleries, marking non-public ones with [non-public] and password-protected ones with [locked].... (more)

Can a non-public image be in a public gallery?

Yes. A non-public image can be in a public gallery. When editing an image, you can decide whether an image is public by checking or unchecking the box next to "this image is publicly viewable". Even in a public gallery, if you uncheck this box, the image itself will be non-public and will only show up to the image owner.