I am also interested in how walking is beneficial to the mind and soul, and also for creativity. When I head out to my local nature reserve, or along the fields and over the hills, my body and breathing fall into a natural rhythm. A C Grayling, the philosopher, has said, "To walk the country lanes and hills is to fall into step with the rest of nature; that is the pace of the cattle and the crops, the breeze, the shifting clouds ... walking, therefore, is good for one's sense of proportion. That, in turn, is good for one's mental health." Certainly, the mind seems to release its hurried, harried ways, and I agree with Henry Thoreau who once wrote in his journal, "Methinks that the moment my legs begin to move, my thoughts begin to flow."
When walking, the mind seems to do two really useful things - it can either rest a bit in the moment, noticing the environment with its sights and sounds and smells (which is really a form of active mindfulness), or it has time to ponder, undistracted, upon issues that matter to us at the time. On most walks I do a bit of one and a bit of the other, often flowing naturally between the two.
Importantly, the brain is allowed to exhale a bit from the dreaded multi-tasking, to think of nothing at all bar the visual stimuli of sky and land, or gently explore things that have been bothering/interesting us. I certainly feel like this is the time my brain can breathe along with my lungs! Indeed, walking at one's own pace creates an "unadulterated feedback loop between the rhythm of our bodies and our mental state...when we stroll, the pace of our feet naturally vacillate with our moods and the cadence of our inner speech." (F. Jabr, New York Times).
The beauty of leaving home or office is that this is truly time that we press the pause button on all our normal activity and duties - we intentionally set aside this time away from the busyness of the world, and for that time life really cannot make most of its usual demands of us. We are physically free of normal constraints and responsibilities, indeed for that period of time we are 'lost to the world' in our walking. We step off the carousel of our busy lives and into our interior life whilst inhabiting those physical, green spaces. This is ridiculously valuable I have found. There is power in not being at the mercy and whim of the pc, telephone and doorbell, there is a reclamation of who we are without all those activities? For this reason, I do try really hard to turn off my phone, perhaps checking a couple of times for missed calls mainly because I have kids at school (you may have other reasons), but the walking is so much more powerful if the scrolling, checking and social media interacting is put aside.