Labyrinths were at first seen by Christians as metaphors for sin and the powers of Hell. The Virgin Mary was seen as the one who leads us from the pits of Hell by pointing toward her Divine Son. To enact this metaphor, one would start at the center of the Labyrinth, and thus, that person would then be led by Mary out as she would bring the traveler safe to Jesus.
Interestingly, this metaphoric reality can be seen in Chartres Cathedral; the Chartres labyrinth is situated at the Western end of the nave (main aisle) the church, and it has the same dimensions as the rose window, which is as high up on the facade as the labyrinth is away from the West wall. If you could fold the cathedral over onto itself as if it were hinged where the West facade and floor meet, the rose window depicting Our Lady would line up perfectly with -- and cover -- the maze.
Though originally seen as metaphors for the dark powers of Hell and our need to rely on Our Lady to show us her Son, over time labyrinths came to be seen quite differently. During the Crusades, when Christians couldn't make visits to the Holy Land, labyrinths came to be used as substitute "Chemins de Jerusalem." Christians, barred from earthly Zion, would walk the labyrinths, often on their knees in penance, meditating on the Passion of Our Lord Jesus Christ; thus making a substitute pilgrimage to the Holy City.
It is believed that in the Middle Ages, there was a bronze depiction of Jerusalem placed in the center of the labyrinth. This substitute journey was quite an undertaking! Consider this, the paths of the Chartres labyrinth, for example, make for a journey of 858 feet. Imagine walking on your knees on cold, hard marble for almost the length of three football fields! That would be quite a journey and workout!
Due to this way of approaching the labyrinth, the classical name "labyrinth" gave way to the name "Chemins de Jerusalem" or "Rue de Jerusalem."
When looked at now from the perspective of making a journey to the center/Jerusalem, the position of how the labyrinth was to be undertaken was reversed: the center of the labyrinth was seen now as the goal -- physical Jerusalem or the Heavenly Zion -- instead of that which is to be escaped -- the pits of Hell.