The idea is that you make a spiritual pilgrimage to each of the scenes of Christ's suffering. It enables the faithful to make a virtual pilgrimage to the holy places of Jerusalem. One may sing the hymn Stabat Mater Dolorosa as one passes between stations. Notionally the Virgin Mary made this circuit (for real) after the crucifixion.
You can earn indulgences (Afterlife air miles) for doing the Stations.