Press the play button to see the video. This video is hosted on youtube.com. When a viewer of your website plays thus video, they are getting the video directly from youtube. You do not use your website's monthly bandwidth allotment. Since the video is not actually stord on your website, you also do not use any of your website's disk space allotment.
The advantages of embedding youtube videos on your wensite include less youtube advertising clutter and complete control of what is presented to your site visitors.