Totally unscientific, but my personal theory is that exposure to different visual / audio stimulation can make the brain jump to different paths when working on

Totally unscientific, but my personal theory is that exposure to different visual / audio stimulation can make the brain jump to different paths when working on different problems, and taking a walk makes me experience more stuff than I will by sitting in the same chair all the time. The brain doesn't seem to work well in a vacuum, so if you spend all day staring at the same four walls, it might let you focus, but there's not a lot of entropy coming in to make you think in different ways.