The pen given by William Minerva in "The Promised Neverland" is significant because it serves as a symbol of hope and guidance for the children escaping from the Grace Field House orphanage. It contains clues, hidden messages, and a map that help the main characters navigate the dangerous world outside and seek freedom from their oppressors. The pen plays a crucial role in helping the children uncover the truth about their existence and the dark secrets of the world they live in, ultimately leading them towards a path of liberation and redemption.