The modern world has convinced us to divide our time into discrete blocks labelled "work," "play," and "sleep." Of the three, only one is completed in the workplace. In our 24-hour day, we are not permitted to shift between these blocks or mix them. Thanks to his position as President, Lyndon Johnson was able to take an afternoon nap without fear of repercussions from his superiors. Most of us don't have this option at all.
Our brains use a variety of processing methods as we become competent in a field. As Barbara Oakley explains in A Mind for Numbers: How to Excel in Math and Science (even if you flunked algebra), you can excel at math and science even if you've never taken a math class. There are two general ways of thinking in the human brain: "focused" and "diffuse," and both are important and necessary in the learning process.
We need time to assimilate new information and incorporate it into our existing knowledge as well as being in a focused mode when learning. To expand our web of neural connections, we require room to process what we're learning. The diffuse mode comes into play here.
When you let go of your focus and let your thoughts to wander, you enter the diffuse-mode of thinking. The brain's diverse regions can communicate with each other, resulting in new ideas. Preliminary thinking in the focused mode typically leads to diffuse-mode insights.