That is Lourdes, a small town in the French Pyrenees, where in 1858 Our Lady appeared to the young peasant girl Bernadette Soubirous. Curiosity and fascination grew steadily, a shrine was erected at the grotto where Bernadette experienced these visions, and Lourdes became a worldwide attraction. Today, more than 4 million people visit the shrine each year. Many come out of desperate hope; and countless "miracles" and healings have been claimed by visitors during the past century.

What is behind the phenomenal growth of Lourdes? Who...