Commercial/private SSL certificates are signed by trusted Certification Authorities. These organizations guarantee the content on websites using their certificates is correctly encrypted.
Therefore, if your website contains unauthenticated content (i.e. it contains both secure and non-secure items), the page you access via the secure HTTPS protocol cannot be verified.
If you are using a CMS for your website, you should check its settings in order to configure all links to work with your SSL certificate.
If you have a static website, you should modify all items you have in your pages to be accessed via HTTPS (images, Flash animations, movies, JavaScripts, external links, etc).
Once all items on the pages are accessed through a secure connection, Firefox will correctly show your SSL certificate issuer next to the "Verified by:" field.
