Here's something that's happened to me quite often... I'm sitting at my desk writing and I'm stuck with some kind of problem in moving forward: it might be a conceptual difficulty, trying to figure out the logic of an argument and meeting some obstacle that I can't see how to get round; or it might just be that the thing's not flowing or that, even though I know the argument I want to make, I'm finding it hard to express it in its most compelling form. So after a while of trying, I decide to sack it for the day and go out for my walk. And while I'm walking, sometimes only a few minutes in, bingo! I see something which I've failed to see for whatever length of time it was that I was stuck with the problem at my desk, and it gives me a clear way forward. (For walking here, substitute jogging in other, younger days.)
This may not be strictly relevant, but it seems at least obliquely so; it reports some research showing that memory performance can be improved whilst walking. The researchers aren't sure why that should be, and neither am I. But I tend to think of it - at least for the case as I've described it - as 'clearing the head'.