to go, pass, or make one's way toward a place or a state
This is the word's oldest and most physical use: something moves along a path. A lump of food travels down through the body; a person makes his way toward a destination. The idea is directed movement, not just being somewhere.
The same picture stretches to movement toward a state rather than a place. To "come to repentance" is imagined as a road the person travels, arriving somewhere he had not been before. Even when the goal is inward, a faint sense of a journey stays under the surface. The ordinary Greek verb for plain traveling was πορεύω; this word keeps the extra flavor of steadily making one's way through or into something.