Originally based on the story of the Mayflower at least according to Steve Harris himself this song with both Celtic and Oriental sonorities is essentially about any journey undertaken to find a better place, a better world. The "coming to America " is illustrated in the sentence "pilgrim sunrise, pagan sunset", which evokes quite obviously both a westward journey and the arrival of a religious community in a "pagan land", as well as the waning of the beliefs of the inhabitants of this land.
Although they were a bunch of religious zealots that England didn't tolerate anymore, the pilgrims of the Mayflower constituted a real "kingdom of heaven to hell", as the hardships of their new life on the American continent almost killed them all (their first winter, 162021, saw the death of about half of the colonists). Regardless of their beliefs, the real miracle there was not "changing the water into wine", but their sheer survival in the extreme conditions they encountered.
It has also been mentioned that this song could also somehow related to the crusades, due to the oriental sound of the music and the line "holy battles take their toll". However, there aren't any other elements in the song that could indicate that the pilgrim in question is a warrior. The notion of landing onto a new world seems to make more sense when you consider the song as a whole, although it could rightly be argued that the crusades were also about arriving into another world. The song needs therefore to be interpreted in a more general way than just a particular era or historical event.