Stepik uses Vimeo for storing and playing video content. In the majority of cases if you experience problems with playing a video it's enough to wait for some time and then start the video again.
You can check whether Vimeo is working properly here: http://www.vimeostatus.com/. If the service is not working properly you will see red or yellow on this page instead of green.
The errors in video playback can also occur because of the issues with your internet provider or the number of students trying to play the same video, as well problems with your device or the video itself.