Having taken neuroscience courses for interest in the subject, the holes in our knowledge far exceed the knowledge - even if the introductory book is over a thousand pages (but that's how it is in most fields these days, and yet you only learn basics).
For example, only very recently we found that the brain literally cleans itself (by flushing) during sleep (http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3880190/). You can bet your Tesla (if you have one) there are lots of mechanisms for physically cleaning up and regeneration that we have no idea yet that they even exist. It's also recent that we find that the various glial cell types in the brain actually help in computation and are not just "helpers" you can leave out when considering brain activity.
I know for myself that when I lie down even when I am not tired (and I rarely am during the day) my brain after a while starts doing some really weird stuff. It's literally like day-dreaming. I have no conscious control, I just let it flow - but I'm not asleep, not one bit. That lasts for 5 to 20 minutes. Afterwards I feel incredibly refreshed. Again, there is no sleep involved, not even half-sleep, so it's a very different mechanism.
All processes are physical in the brain in the end: Even electrical activity is performed by ions, not by electrons, after all. So even electricity is physical movement of atoms, unlike in human-made electrical equipment where it's just electrons for the most part (you see the effect when it's ions in batteries, if you open them when they are old, while a copper wire doesn't change even after years of current flow).
In addition, part of electrical activity performed with ions is the transmission to another cell (within the brain mostly other neurons, of course), which is purely chemical through various transmitters. When I first heard about that I thought "couldn't this be optimized in a human-made system to stick to using only electrical signals, it would be sooo much faster". However, I quickly abandoned that thought, those transmission being 100% chemical is a major part of the information processing. Human-made computers show you can do make something "purely electrical" - but then it works following completely different principles. The chemical vector adds a huge flexible component to the system, it enables the majority of what the brain is and can do. But it means that a huge chemical factory has to be maintained: A gigantic amount of molecules needs to be synthesized and broken up continuously, and vast amounts of it. And while you don't need to do much cleanup except for dust in a computer because it's all just electrons, the brain is less electrical than a chemical factory.
Even the electrical activity which uses just simple ions, so they are always there and don't have to be manufactured, uses a lot of energy, because the gradient has to be maintained by physically moving ions back out of the cells to establish the resting membrane potential. That energy comes from ATP, which first has to be produced. In a human-made system we simply provide the electrical field to the entire system from the outside, and the dirty chemical processes have been outsourced to power plants somewhere far away. In the brain you have all that waste-producing activity right in each cell!
Add to that that there is so much activity in the brain, much more than in most other tissue in the body, and you can see a lot of "house-keeping" has to be performed. And that is an area that we still know precious little about. So it seems plausible that occasionally heavily used parts of the brain may want a little rest - during which they don't really rest, they just do cleanup and maintenance.