A pilgrim is a person who goes on a long journey often with a religious or moral purpose, and especially to a foreign land.
After the Mayflower arrived, the first baby born was a boy. His parents (William and Susannah White) named him Peregrine – a word which means travelling from far away and also means pilgrim. The writer of Mourt’s Relation in 1622 refers to the Plymouth Colonists as pilgrims. Governor William Bradford calls the Plymouth settlers pilgrims when he writes about their departure from Leiden, Holland to come to America: “They knew they were pilgrims, and looked not much on those things, but lifted up their eyes to the heavens, their dearest country; and quieted their spirits.” Governor Bradford also wrote a poem in which he refers to himself as a pilgrim.
“Pilgrim” became (by the early 1800s at least) the popular term applied to all the Mayflower passengers – and even to other people arriving in Plymouth in those early years – so that the English people who settled Plymouth in the 1620s are generally called the Pilgrims.