There are several different types of meditative walking, from various different spiritual traditions.
The theologian St Augustine famously wrote “Solvitur ambulando” (It is solved by walking), by which he presumably meant that as you walk, the problems that were at the forefront of your mind are put on the back burner and there solved. I have experienced this process myself.
Walking is also more environmentally friendly than other means of locomotion.
Eastern Orthodox Christians practice the prayer walk, which is a form of processional walking, with stops for prayers at various intervals.
The practice of walking labyrinths is a very ancient practice dating from pre-Christian times, but also used by Christians in labyrinths such as the famous one at Chartres. In a Chartres-style labyrinth, you never know quite how near or far you are from the centre, so as you twist and turn through the labyrinth, walking slowly and meditatively, you are reminded of the twists and turns of life, and sometimes solutions to problems come to mind as you walk.
Buddhists practice the walking meditation, which is where you walk slowly and mindfully, place one foot in front of the other in a slow and deliberate way, silently reciting a mantra as you walk.
Another way of walking mindfully is to walk in a garden, and walk towards the first thing – perhaps a plant, perhaps a stone, or a leaf on the ground – that attracts your attention, and then really look at it. What colour is it? What is its texture? How is it structured? Is it growing or decaying? Smell it, touch it. Does it make a sound? Follow the patterns on its surface. When you have really observed it with all of your senses, thank it and move on to the next thing that attracts your attention. At the end of your walk, you might like to draw what you have seen, or write a poem (perhaps haiku) about the experience.