It sounds as though you may have a bad video driver. The screen you are seeing is called the Blue Screen of Death (not technically of course) but usually happens when you have faulty hardware or a bad driver. These errors are commonly called Stop Errors because it halts Windows and doesn't let you get any farther without a reboot.
Many times you won't even be able to recover from these and will need to research the error details to see what the problem is. Since yours happens when you watch videos I would first try to update your video card driver. If you don't know the make and model of your video card then you can go into Device Manager to find it. Then you can do a search on the manufacturer's website for your model of video card and download the one for your version of Windows.
Another test you can do is try your videos in a different web browser such as Firefox or Chrome to make sure it's not software related. You can use multiple browsers on your computer without having to choose only one. If none of those options work then you will have to write down the error code and do a little research.