Chapter 12 of White Space is Not Your Enemy covers storyboarding, as well as going over how to create different types of shots and other photo/video aspects in detail. If you've ever looked at extras or behind the scenes from movies, you've probably seen storyboards. You can also think of them as a comic/graphic novel version of your project (in condensed form, of course).
Storyboarding is the equivalent of an outline you'd do for an academic paper, report, short story, or novel. It gets all your main points and thoughts out in a logical, organized order. Storyboarding also includes visuals - at early stages, this can be quick sketches or notes, and at later stages this will be draft images or final copies if you have them. It should also include brief notes so you remember where you're going with the project, don't forget important details, and can clearly communicate your ideas with your client.
For a personal storyboard form doesn't really matter as long as you can utilize it as a production tool, much like a writer's outline. Everyone forms ideas and works differently. However, a professional storyboard that you will use with a group and show to a boss or client should be formatted appropriately - nothing huge, just ensure that all necessary information is there and looks professional, such as your name and the company name, the client name, the project/purpose, your/your company's logo and contact information etc.
Storyboards are especially helpful for those of us who think visually. Sometimes it's a lot easier to draw something out than to explain it. It's also often easier to communicate ideas with group members visually, so you know you're all on the same page.