They found that attention seemed to be linked to boredom, whether it was or wasn't called out explicitly in the experiments themselves. When people are unable to engage their attention in the task at hand, they start to feel bored. When tasks are too simple to require focused attention, people can't find a suitable point of engagement and not enough effort is expended to maintain the focus on the activity at hand. Trying to process an overwhelming environment with limited attention can also make people bored because their attention is being pulled in different directions.
My first reaction to this is: boredom is God's way of telling you to exercise your creativity. Find something to exercise your mind!
On second thought, when people are stuck with tasks that are boring, there is probably a structural issue and managers should go read Sayers on good work.
On third thought, sentry duty at 3:00 is both important and irreducibly boring--until it suddenly isn't boring.
And then again, some of the boredom they find arises when the task is too complicated, not too easy. So it isn't just a matter of locating enough Epsilons to fill the necessary roles.
And still again: Two kids in the woods; one bored and cranky while the other is a bird lover avidly watching for his favorite birds. "Genius is an infinite capacity for taking pains?"
So maybe there is something important we can Oh look, a squirrel!