It's interesting how the entire attitude toward walking and physical exertion in general differs between the West and developing countries. Like someone said before, our bodies were made to walk, yet us lucky folks living a sedentary lifestyle often struggle with that concept. I am continually amazed by people who'd rather drive to a grocery store just behind the corner than take a quick walk that probably takes less time than getting in and out of the car.
It has been a sobering experience to spend time with people in the less developed regions of the world who can't afford the privilege of a comfy modern life. Ordinary people who routinely walk 5, 10 miles to work every day. In heat, rain, cold, sandstorms, whatever. Frail old ladies carrying huge burdens that would break the back of any fitness buff working out at an air-conditioned gym.
I guess long distance walking is really more about the mental attitude than physical fitness alone. Unless you have some sort of disability you're probably capable of walking much, much farther than you may imagine. The chances are, you just don't know because you've never tried it.
Get in some basic shape to begin with, do some all-around cardio and strength training and 10 miles shouldn't be considered anything more than a casual stroll. Once you get the hang of it, why not try a proper day hike - 8 to 10 hours is perfectly manageable for any reasonably healthy individual. It is a great way to spend time outdoors and helps promote a healthy lifestyle that will reward you in many ways.