Personally i think a good walk helps not just physically but also helps ease ones mind.
When i (run which i do often) it's ussually for my fighting skills, as a boxer i run to litterally pound my leg bones and stretch the muscles working myself into a frenzy.
I run over 10km in the morning and on saturdays i run an extra 5km in the afternoon. When conditioning i also tend to sprint and do crazy excerises like running uphill with a mouthfull of water to help breathe through my nose not mouth. I also run over gravel and woodland paths barefoot. Sometimes i even run with wieghts ussually strapped to my legs and wrists but sometimes heavier wieghts in baskets.
But all this merely helps condition me for fighting. It is only used to push myself to greater levels of endurance. Some might call it torture and boy do i agree! All this is pushing myself to control my body.
But even i take a gentle stroll too. When running i can only focuss on one goal, moving almost blindly and not thinking much about anything. But when you walk you can hear things better like birdsongs and water (i train near a lake) and you see people around you rather than pound past them like a raging elephant.
Walking also helps calm myself down and it means i can take a friend with me and talk normally i run in silence unless i'm shouting at someone to make way. When i walk i can move with grace and i feel like a better person, also i try and walk in quiter places its why i prefer the arrow valley lake..... If you ever come to Redditch in the UK it's a truly beatifull site with plenty to do and see.