Google Sites is delivered over https. If you link to any content on your site that delivers content over http: - and that includes Adsense - your browser may (depending on which one it is and your settings) display a message warning you about insecure content. This includes Google Chrome which unfortunately displays quite an invasive message.
The only way to avoid this is to map a domain to your site, e.g. www.example.com then your site will be available on http: and this will avoid this issue provided the site is public (e.g. view this site at sitesguide.pjrprojects.co.uk). Note that if you are a site owner/editor and sign in to the site or view the site on the sites.google.com address you will be switched to https: and will see the message. Public viewers of your site at the mapped address will not.