Why are storyboards so important for planning a film?
Storyboarding is important because it allows a filmmaker to communicate their vision precisely as they see it to the rest of the cast/crew. Also, it can ensure that no shots are missed or forgotten when filming on location or on set.
Experience as a sketch artist is not necessary. As long as the general points you want to address when filming are present in the storyboard; it will be useful.
How does the script relate to the storyboards?
Storyboards are a visual representation of the script. Also, storyboards can offer more insight and clarification to vague actions, details or emotions described in the script.