This is a nice piece from the New Yorker. I excerpted the health benefits portion below, but the piece ambles back to the connections between walking and creativity, especially writing.
Why Walking Helps Us Think - The New Yorker: What is it about walking, in particular, that makes it so amenable to thinking and writing? The answer begins with changes to our chemistry. When we go for a walk, the heart pumps faster, circulating more blood and oxygen not just to the muscles but to all the organs—including the brain. Many experiments have shown that after or during exercise, even very mild exertion, people perform better on tests of memory and attention. Walking on a regular basis also promotes new connections between brain cells, staves off the usual withering of brain tissue that comes with age, increases the volume of the hippocampus (a brain region crucial for memory), and elevates levels of molecules that both stimulate the growth of new neurons and transmit messages between them.