Was this site previously running as non-SSL or is it a new site, set-up from start to run on HTTPS?
If it’s a migrated site, you’ll need to make sure that any URLs that refer to the site domain and are stored in the database (either part of content – posts, pages, widgets – or plugin settings) have been updated to use the new secure URL. You can also use the browser to investigate which media resources are still loaded via plain http.
If it’s a new site, you may have a bit of content somewhere (actual post/content text, widget, plugin resources, so on) that tries to load its resources without ssl, resulting in the aforementioned warning.