If you want to embed a video from youtube, you can use the <iframe> embeding code. Copy it from YouTube, then go to product page, in the product description field press the "Tools" -> Source code. And paste in the opened window. If you pase it in visual editor, the browser won't read it as HTML, but as a plain text.
In the case of a product description, you are limited to the place where the full description is displayed. With simple widget you have possibility to insert video in different place. You can use the widget zones for it. For example QuickHTML plugin
allows you to insert HTML code into any widget zone.