A rough cut in video editing is exactly what it sounds, it's a rough version of the video.
Editors create rough cuts to share with clients so the client can provide feedback on the video in the early stages of the edit.
Rough cuts usually won't have any graphic elements or animation, they won't have the final music, the audio won't have been edited, and the footage won't be colour graded.
By sharing an early version of the edit, clients and editors can discuss creative choices in the edit to make the best video possible.