It means that information stored in gh-pages branch of your repository will be publicly available via GitHub pages via http://<username>.github.io/<projectname>.
gh-pages branch is special branch, which content is automatically published by mechanism called Github Pages.
Here is an example. I've created private repo private_with_pages. You can not see it because, well, it's private. Nevertheless, file index.html, stored in branch gh-pages, is publicly available.
Now in settings of the github repository I see message “Caution: This repository is private but the published site will be public.”
According to this help page the only way to disable this feature is remove gh-pages branch from github. How to remove remote branch is described here.
See related question: Private pages for a private Github repo