This development follows YouTube's switch earlier this week to an HD-like 16x9 aspect ratio frame. (Videos in the older 4x3 aspect ratio are pillarboxed, with black bars on the sides.)
Clicking the HD link starts the video from the beginning, after a pause of several seconds for buffering (don't even think about watching an HD video on dial-up). The resulting image quality greatly improves the old YouTube experience, but it's not hi-def. How could it be? The YouTube image frame is only 640x360 -- a quarter the size of a 720p frame.
Of course, you can expand that frame by clicking the full frame icon. The resulting image won't rival what you get with an HD television broadcast, but it's a vast improvement over anything you've seen before on YouTube.
The high-definition videos only run from the YouTube page. If you enbed one into your own web page, you get a smaller, low-def version without the HD option.
The additional bandwidth required will certainly add to the cost of running YouTube. Whether it will attract enough additional revenue to offset those expenses remains to be seen.