It's totally possible to be a competent storyboard artist and not know anything about composition. Heck, that describes the first 10 years of my career.
But there are many good reasons to keep composition in mind while you board, and strive to do boards with great design and compostition.
First of all, everybody has a good inherent sense of design. They know it when they see it. They gravitate towards it. So directors - and everyone else - will like boards better if they are well composed and designed. Obviously, the most important aspect of any board is that it be CLEAR. It has to put across the story point first and foremost. If it doesn't do that then nothing else matters! But a well-designed and composed storyboard is like the icing on the cake. There's a reason good packaging helps sell products. When you cut together the story reels on a movie for the first time and screen it at the studio, you're asking the audience to watch 75 minutes or more of story sketch. This is a lot to ask - we humans are attracted to movement and static boards can get dull after a while. Especially if there's no color. You can imagine how that could be hard to sit through.
I know, I know - a good story should be able to be performed with sock puppets against a blue sky and still be great. Of course, we all get that. And good drawings should never be used to sell a story that doesn't work.
But the minute you put pencil to paper (or stylus to Cintiq) you're dealing with composition. It makes your job easier to learn how to compose well rather than trying to blunder your way into a good design.
Here is the basis of all good design - an interesting breakup of space. We humans have a tendency to want to make everything even and straight when we draw. Good design requires fighting this principle! Find a way to break the space into thirds, or fifths, and it will be a lot more interesting.
Don Graham talked a lot about this next principle in his seminal book "Composing Pictures" but back when I read it I didn't get it. Here's a better explanation from the Famous Artist's Course: basically, putting the subject in the exact center of the frame makes for a static and dull picture. Putting it next to the edge of the frame creates a tension between the subject and the edge of the picture that is distracting and undesireable. So put it in between those two spaces - off-center but not too close to the edge.
And here's a helpful farmer to show us the difference between even, dull division of space and breaking it up in an uneven and interesting way.
Pretty simple, huh? I don't know why people make this stuff so hard, but there are very few good design books or books that can explain it in an understandable way. Lots more to come on this subject!