Continuity is important in the flow of the film. If continuity is broken the flow of the film is broken and can turn even the best of films to trash. A continuity error can be something such as in one shot a character is wearing a black jacket and then in the next shot they're wearing a red jacket. It wrecks the flow of the film. Here's a video pointing out some continuity errors in Casino Royal.
The next post is about Basic Editing