First, check your theme options panel in the post editor for a Quality menu (MotionPicture and Ambition, for example) and select HD.
If your theme does not have an HD selector, you will need to tailor your embeds/oEmbed links. You may also be able to set the default from your profile on your video host.
View the YouTube parameter guide
The key is the “?vq=hd720” at the end of the video URL in the embed code. Example:
<iframe width=”560″ height=”315″ src=”http://www.youtube.com/embed/_3rLN6WR3oA?vq=hd720” frameborder=”0″></iframe>
This handy tool can help you customize your embed codes, otherwise read YouTube’s official documentation.
Vimeo requires you to set HD defaults in your profile, which may require Vimeo Plus.
View the Vimeo HD FAQ