The thing is, we have evolved being active, being active is the default setting for humans. Being inactive is really really bad for you, both mentally and physically. Nobody is saying going for a walk will cure depression, they are saying that going for a walk - which is a simple, free and unchallenging kind of exercise, accessible to most people - will help you. Which it will.
The exercise gets your muscles moving (which is what they are designed for, aren't they), your blood circulating, oxygen washing all over your systems, taking deeper breaths, feeling the wind on your face. Then you have the change of scene, hopefully seeing some nature which is usually beneficial. Even in towns there are gardens or house fronts to look at - I find just seeing the different ways people have chosen to do their house decor or gardens interesting. You're getting fresh air too.
I often take a flask of tea with me on longer walks, I don't always need it but it's comforting to know it's there. Putting my flask in my backpack alongside a rainhat and other bits and bobs is part of the preparation, a push towards getting out. I often walk with a friend which is also much nicer if they are like minded to you, a companion can make it seem like the sun has come out and is another element of a beneficial walk. But if you prefer to be alone that's totally doable too.
I always feel better after a walk, just because I've done something positive. But I also feel refreshed and more inclined to keep moving, so it's a win in that respect too. A small win, but it all counts.