A pilgrim is one on a journey to a holy place. The New Testament refers to Christians as “strangers and pilgrims on the earth” (Heb. 11:13), and 1 Peter 2:11 uses almost the same words.
The first Christians believed their destination was a holy place, heaven, so their time on earth was only a journey.
The English Puritans who settled at Plymouth, Massachusetts, in 1620 became known as the Pilgrims because they believed they had left the corrupt church in England to live in a new land and build a holy society.