In recent years walking the labyrinth has become a significant spiritual practice for many people, both Christian and non-Christian.  In pre-Christian Europe labyrinths appear in Neolithic and, later, Celtic cultural contexts.  At some point they were "baptized" by the church and incorporated as an element of contemplative spiritual practice.  They may be found in a number of medieval cathedrals; probably the most famous, serving as the model for many modern recreations, is the one from Chartres cathedral, pictured above.

When I walk the labyrinth, I feel as if it is a recapitulation of my own journey on the contemplative path, one that is probably common to many people.  When you begin the journey, there is an initial flush of enthusiasm, so that you get close to the center--where God is present in a perceivable way--without quite reaching it.  Then you are pulled away and spend time enduring long stretches where the whole business seems an act of futility.  With patience, you eventually reach the center, however briefly.  But you are not meant to stay there for good--in this life, anyway--and so you retrace your steps to return to the "real" world, hopefully refreshed and nourished spiritually.  I usually recite the Jesus Prayer as I walk the labyrinth.

A good article on the labyrinth, albeit from a largely secular perspective, may be found on the always-interesting Aeon website.