Normally the youtube url looks like the one below which gives you low resolution 320×240 videos.
Simply add &fmt=6 onto the end of url
Now you should see high resolution videos. If no change is observed, then it means the video has not been converted to the higher resolution yet. View the video in full screen mode to see the difference.
If you add &fmt=18 to the end of url.
Now it will play the high-resolution 480×360 MP4 high-bandwidth videos with higher quality audio when available, otherwise it will play the regular version. Give it a try.