When you watch a video on YouTube it has to actually download it from the internet to your computer before it can play it.
Normally it starts to download it, then once enough has downloaded it starts to show it.
As long as it can DOWNLOAD it faster than you can WATCH it then you are fine.
If you are WATCHING it faster than it can DOWNLOAD it you get the stop start action.
If you have a very slow broadband line, or if you are using your broadband to do other things at the same time as watching the YouTube video, then this could cause the problem.
If you have a slow broadband line there is not much you can do.
If you ARE doing other things then you could stop doing them (maybe downloading a film?) and then YouTube will speed up.
By the way, as you are watching a video the RED line at the bottom is showing you how much it has downloaded.
The circle that moves along shows you how much you have watched.
As Ethel says, if you press pause and IF you are willing to wait till the red line is all the way to the right then that means the whole video has downloaded and you will be able to watch it without the stop starts.