Philemon is a benevolent spirit who bestows Personae to people, he resides in the realm "between consciousness and unconsciousness".
He physically resembles a tall man wearing a white mask. In the waking world, his presence is indicated by a golden butterfly.
Philemon operates as an ally to the party, despite the fact that he can only watch events unfold as a neutral observer. As such, he cannot directly interfere with anything that is going on. Philemon is conducting an experiment with his rival, Nyarlathotep, over humanity's destiny. Philemon believes they can become enlightened, higher beings, but Nyarlathotep manipulates events to ensure mankind's destruction.
In Persona 3's Hermit Social Link, as well as references to the Joker, Maya and Tatsuya, when the protagonist begins the game, an automated script named PHIL welcomes him. This is most probably a reference to Philemon.