Communicate your ideas effectively
Most peoples minds operate mainly visually. They might have a lot of other stuff to think about, so you can't really expect them to imagine your idea when you are trying to tell them with just words. Illustrations are a quick and affordable solution.
Save a lot of money and headaches
Just as an architect plans a building on paper or a musician puts down his music on paper, it is highly recommended to do the same with film. Preparing a shoot with storyboards is much cheaper and quieter than improvising on an expensive set.