Story structure
Wise old man
A Jungian archetype and classic literary figure: the sage, wizard or hermit whose wisdom guides the hero, as Gandalf and Merlin do.
The wise old man is "an archetype as described by Carl Jung, as well as a classic literary figure," a profound philosopher "distinguished for wisdom and sound judgment." Jungian psychology also calls this archetype the senex, and in individuation it appears late, after the anima and animus are worked through, as a "masculine initiator and guardian" signifying the Self. In stories he is the kind elderly father figure, wizard or hermit whose knowledge of people and the world guides the hero and explains the meaning of the hero's encounters; Merlin, Gandalf, Dumbledore and Obi-Wan Kenobi are the standard examples. The article also notes the craft move built into the role: the figure is "often temporarily removed so the hero can develop independently."
That removal is the mentor's structural job: he arrives at the Meeting the Mentor step of the Hero's Journey and must step aside before the ordeal. Casting and varying him is covered in twelve archetypes for writers.