The wise old man archetype in mythology represents knowledge, guidance, and experience, often embodying the voice of reason in narratives. Examples include figures like Gandalf from Tolkien's works or Moses in religious texts. These characters act as mentors to heroes, providing wisdom and insight that facilitate personal growth and enlightenment. Their presence emphasizes the significance of mentorship and the transmission of oral traditions, guiding the next generation through challenges and inspiring them to achieve their potential within mythological narratives.