Only a few sites register for an Extended Validation SSL (EVSSL) certificate. For those certificates, you'll see the company name next to the padlock in the address bar. Regular secure certificates do not prove ownership, so Firefox displays that message about the owner. It's usually not a problem unless you were used to seeing the company name there before.

More importantly, do you get a solid green padlock? This article describes the different icons that can appear in that area: How do I tell if my connection to a website is secure?

No green padlock. Gray with triangle, as described here:

https://support.mozilla.org/en-US/kb/how-do-i-tell-if-my-connection-is-secure#w_gray-padlock-with-yellow-warning-triangle

What I had difficulty understanding is that - this is Yahoo Mail, not some corner shop website, and - the site is HTTPS and yet the page above says that my communication is not encoded.

Maybe this is not a FF issue, but it is scary.

You can see a special padlock at the left end of the location/address bar.

• a padlock with a strike through means that mixed active content is blocked.
• a padlock with an exclamation mark attached means that mixed passive content (e.g. images) is present, but not blocked.

The shield icon, previously used for mixed active content, is now used for Tracking Protection.

• https://support.mozilla.org/kb/mixed-content-blocking-firefox
• https://support.mozilla.org/kb/control-center-site-privacy-and-security-firefox

You would have to contact Yahoo if they include content coming via an open connection on a secure page.

You can check the log in the Web Console for error messages about mixed content to see what it is about.

• https://developer.mozilla.org/Tools/Web_Console

If necessary use Ctrl+F5 or Ctrl+Shift+R to reload the page and bypass the cache to generate a fresh log.

If you are viewing a page with "user generated content" or email message, often the user inserted it with a plain HTTP link instead of a secure HTTPS link. In that case, Firefox will retrieve the image and show the mixed content icon. There may be another explanation, but I think that's the most likely.

Thanks all.

I think I have understood it now.

PS I can only chose 1 answer as being the solution, but cor-el, your answer was good too.