Is your internet connection slow? That could be the problem, maybe the video is "buffering" (when I used to have a slow internet connection a few years back, that would always happen, and that pi##ed me off a lot).
Or maybe it's a site error, YouTube could be down right now. That's probably not the case though, as it worked for me when I was on awhile ago.
Lastly, it might just be the video you chose. I've noticed on a few occasions that has happened to me. Try a different video and see if it works.
Mike J provided a great answer but on a side note, while the video is buffering hit the arrow keys on your keyboard and it will turn into a game of snake for you to play while you wait for the video to load!
