It might seem like it's doing nothing, but what you computer is doing is downloading the video file so you can watch it. It has to download it to temporary storage on your computer so it can play the vid. Depending on your connection speed and the size of the video, this could take anywhere from 30 seconds to several minutes.
Alternatively, you can just right click the "Video" link and click "Save as" to download it, then you can open up your media player and play it whenever you want.
