If you are really willing to think about it, boredom is not about having nothing to do. Boredom is about not having anything "challenging" or "interesting" to do. One may have something to do, and yet feel bored, because that "something" is mundane or simply normal. Normal is, apparently, boring.
Moreover, there is never a time when one does absolutely nothing. Even though we may not be physically active, our mind is alive and kicking at all times. Yes, day-dreaming, scheming, imagination running wild etc., are the result of the so called state of "boredom". Bacause the mind is a massive processor, which cannot stay idle. Give it something challenging to chew on, and it will be happy. Give it something interesting to ponder about, and it will be pleased. When we don't challenge it, it becomes self-employed. It flows, naturally.
This flow has great potential. Sometimes the so called "day-dreams" offer sub-conscious solutions to problems. They can be used productively. It all depends on ones perception. I dont want to get too scientific or too philosophical about it in this blog. But I would seriously suggest that when you are bored, follow your mind. Watch it carefully. Observe the patterns, the schemes, the fragments of imagination that make up your train of thoughts. You might just discover somethihg astounding.