Its up to the DM exactly how it functions, hwoever if i was running it:

The player would have to physically travel. Animals would be too scared of the warping of reality to be ridden for the journey. You wouldnt be able to start it if you couldnt travel the entire distance. When walking your mind is not focused on the road around you, but if an encounter or something happens while walking you find yourself in some kind of extra dimensional plane, maybe a road that goes infinitely in both directions and to the left and right just seems to dissolve right outside of your field of view. (like the infinite staircase from 3.5) Anyone seeing you depart would see you fade off into the distance as you walked away, dissapearing long before you should over the horizon. Likewise anyone seeing you arrive would see you fade into view as if you were coming over the horizon, though much too close.