Go to the following link to create the code for HIGH QUALITY embedded YouTube videos.
Follow the instructions on the web page.
You can test this quality improvement directly on YouTube simply by adding the following text directly to the end of the video url &fmt=18
The code that you generate from the above web site will allow you to embed the high quality Youtube video to your site. Viewers of your video will see the video in the best possible quality vs the standard... not so goo quality. The difference is significant.