Pilgrimage is the technical term for a journey, usually of a voluntary nature, to a site of particular significance, generally of religious significance. One engaged in this practice was called a Pilgrim.
The purpose of a pilgrimage was to cleanse the soul of sin, and the further or more difficult the pilgrimage, the greater the spiritual benefit. The main Christian pilgrimage(s) in period were to the Holy Land, but pilgrimages also took place to other places: to Rome, to tour holy sites and perhaps see the Pope; to the tombs of saints or martyrs; or to battle sites, where great victories had been won, particularly against non-Christians or heretics.
In period, the crusades were regarded as a sort of armed pilgrimage, and all crusaders arriving in the Holy Land would fervently pray at various holy sites before and after battles against the "infidel". Indeed, the First Crusade was, at least in part, launched as a method of guaranteeing Christian access to Jerusalem and its environs.