First of all you can use the HTML snippet widget to insert a youtube video. Just put the standard youtube embed code in there.
You can also generate this embed code with a custom youtube link in Mendix, and render it using the Rich Text Viewer on HTML mode.
Reaction on comment of Ravi on Robert's answer:
Upload your own video to youtube? You can retrict the access to your video in the upload settings. Or you need to host your video somewhere else and use the html code implement in the HTML snippet.