When a secure (https enabled) website is displaying a caution on the certificate and warning about mixed content, you need to identify and correct the content on the page that is causing thje warning.
A good check is to visit https://www.whynopadlock.com and enter the URL of the troublesome site. It will quickly identify the elements – typically images – that need to be corrected.
If the images are on the same site you can usually just change http:// to https:// in the image URL, or alternatively remove the http://mysite.com from the url of the image. If the image or element is on another site you can try changing the protocol to https, but you may have to bring the element onto your own site or live with the warning. Just just accepting the warning is a bad idea because it caused your audience to lose confidence in your site.
Another good discussion of this with additional options can be found at ManageWP, it's worth a read.