SYMPTOM
When you embed a video on a secure page - you may find the video displays as just a blank placeholder box like this (or similar - dependant on the browser you're using):
REASON
If your website is using a Secure SSL Certificate to protect your website - all pages and URLs on your site will start with "https://" and typically show a lock-type icon next to the URL e.g.. 
Most browsers these days require you to link to all pages as secure pages if you're already on a secure page, otherwise the browser may try to limit the data and content that you're able to see and access from the secure page - again - in an attempt to protect your browsing session.
SOLUTION
You'll need to update any custom links, image references or - as in the case of this article - YouTube embed codes - so that instead of using: http:// - it needs to have the full secure https:// in front of the URL.