Let's take a look at the default embed code for Blackbaud's NetCommunity Spark Overview YouTube video:

<iframe width="560" height="315" src="//www.youtube.com/embed/WgDMBeoAQ_M" frameborder="0" allowfullscreen></iframe>

As you can see, the video is inside an HTML <iframe> tag, which will "embed" the video itself inside an invisible frame.
When you add this code on your website, we recommend adding it into an Unformatted Text part. This part will render the HTML code on your page and apply the values set in the tag's attributes (like height, width, src, etc...).

The "src" attribute is the video's source, which is a URL. This URL must be copied exactly as is from the video's site (YouTube, Vimeo, etc...).
If you add an "http:" in front of "//www.youtube.com/embed/WgDMBeoAQ_M", the vidoe will NOT display on your website.

If you notice this symptom with one of your embedded vidoes, simply check the code when in edit mode of the part it resides in.
If you see "http:" in front of the source URL, simply remove it and make sure you only see "//" in front of the URL.