Like the Good and Bad Angels, the Old Man is an allegorical character, which means that he's a physical representation of an abstract concept.
What concept does the Old Man represent? Well, consider his words to Faustus: he begs him to stop sinning, assuring him that his soul is still "amiable," or good (5.1.40). He claims to see an angel hovering over Faustus's head waiting to pour "a vial full of precious grace" into that soul. Then he assures Faustus that all of his words are spoken in "tender love / And pity of thy future misery" (5.1.47-48).
To us, the Old Man's words sound a lot like things Jesus might say to Faustus, if he were around to give the guy a talking to. So it's possible that the Old Man represents Christ. But that's just one theory.
He might also represent faith, since the Christian definition of faith involves the belief in God's grace, and that God will save the souls of believers despite their sins, which is exactly what the Old Man tries to convince Faustus of. Too bad he totally fails.