Beyond the common positive physical effects gained from walking it may be that walking and talking heighten the effectiveness of counseling. Taking a short stroll (in plain sight of others) with a Scout and talking through a problem may be better than just sitting or standing while you talk.
From an article on walk therapy:
In some instances, physical activity can be as effective as medication for treating depression, he says, with none of the side effects.
Exercise releases feel-good chemicals that provide post-workout feelings of well-being, and exercise-induced hormonal changes are likely at the root of the more permanent relief from depression that can come from routine physical activity.
I have found that any kind of slightly distracting activity (like washing dishes) deepens conversations. For some reason talk seems more honest and uninhibited.