Storyboards force the director to translate his broad vision for the film into concrete, executable shots. During the storyboarding phase, he can experiment with different camera angles, reorganize scenes or cut them to see how they impact the story. Some directors use storyboards as a reference during production to help them remember all of the shots they planned. They may also use them as a way to communicate their vision to producers or investors.
A storyboard can serve as a paper edit of the movie, which allows you to identify weaknesses that may not otherwise be apparent until post-production. For example, when you "see" your film, you may discover that the pacing is slow, that several visually similar scenes are lumped together or that a particular scene is going to require more props, extras or visual effects than you had thought. Because storyboards are a tool that you can show to others, it allows them to help you identify these weaknesses and improve the film before you shoot it.
When a director communicates his vision using words, other members of the crew may not receive the mental image he had intended. Storyboards allow every crew member to have exactly the same vision. They also provide a reference for the crew to use throughout the film so they can prepare for upcoming shots without having to ask the director to restate his intentions for each one. When the crew knows what kinds of shots to prepare for, they can prepare more efficiently and appropriately.
Time is a precious commodity on a film set. Each minute is worth hundreds or thousands of dollars in salaries and equipment rentals. Storyboards allow key crew members to make decisions in pre-production instead of taking time during production. It also helps the director avoid shooting useless footage or having to pick up additional footage at a later date. It may help prevent mistakes, rushed judgment calls and miscommunications, which increase the time and money used on the film. The better prepared the crew is, the more streamlined the process can be and the cheaper they can make the film.