In Greek mythology, Orpheus was the son of Thracian king Oeagrus and the muse Calliope (some versions have Orpheus' father as the god Apollo). Apollo, fond of Orpheus, gave him a small golden lyre, which he quickly mastered. Taught to sing verses by his mother, Orpheus was so skilled at making music that he was called "Master of Strings" and "Father of Songs", capable of such music that even rocks and animals would be compelled to dance.
Upon the death of his wife Eurydice, Orpheus was so distraught that his mournful singing brought nymphs and gods to tears. Traveling to the underworld, he used his music to soften the hearts of Hades and Persephone, who allowed him to bring his wife back to the upper world on the condition that he walk in front and not look back until they had both arrived on the surface. In his anxiety, Orpheus forgot his warning and looked back when he alone had reached the surface, and saw his wife vanish, this time forever.
At the time of his death, Orpheus had become an apostate, spurning all gods save for Apollo, whom he thanked for his golden lyre. For this he was ripped apart by Dionysian Maenads (although according to other versions, he is ripped apart for refusing to participate in their drunken (and often cannibalistic) orgies, on account of remaining committed to his lost lover), only his head and lyre remaining. His head floated down the Hebrus, continuing to sing sad songs until it was buried on the island of Lesbos, while his lyre was carried to the sky by the muses and placed among the stars.
True to his legend, Orpheus is the archetypal musician in literacy and lore, and he stands for foolish human folly (for turning back out of doubt) as well as sacrifice (for dying for Eurydice).
"A poet of Greek mythology skilled with the lyre. He tried to retrieve his wife, Eurydice, from Hades, but she vanished when he looked back before reaching the surface."
—Persona 3 compendium
Orpheus is a Lv 1 FoolPersona, and is the initial Persona of the protagonist. He makes his first appearance during the protagonist's attempt at summoning a Persona via the Evoker to fend off the looming Shadows. During Orpheus' initial summoning, Death (whose appearance is identical to Thanatos) bursts forth from Orpheus' head, ripping him apart in the process. Death violently destroys the Arcana Magician before reverting to Orpheus, who then becomes accessible to the protagonist.
Orpheus' grotesque introduction signifies the fate he suffered long ago. According to mythology, he was ripped apart by Maenads for not honoring Dionysus, leaving only his head untouched. This is the reason why his body is entirely mechanical and why his voice is processed through a speaker embedded in his "stomach".
Should Orpheus' appearance be compared to the protagonist, they have the same face. His lyre's shape resembles the chair the player sits on when entering the Velvet Room.
If the player chooses the female protagonist in this game, a female version of Orpheus becomes the player's initial Persona as to reflect on the player's gender, though the female protagonist's versions of Thanatos, Messiah and Orpheus Telos retain their masculine appearance.
This version of Orpheus, although bearing the same concept as the male counterpart, now sports longer brown hair, a golden-colored torso instead of a platinum one the male Orpheus adorns and a giant heart-shaped lyre.
The female Orpheus may be obtained and used by the male protagonist via New Game Plus, should the player have registered the female Orpheus in the compendium while playing as the female protagonist. The same is true for the reverse, with the female protagonist having access to the male Orpheus.
Orpheus (regardless of the protagonist's gender) will now give the player the Skill Card "Agi" after Orpheus reaches level 3.
In the playable epilogue of Persona 3 FES, titled The Answer, Orpheus becomes Aigis's Persona.
During a heated battle against Metis, Aigis summons Athena. At the same time, she awakens to a new Persona and Athena metamorphosed into Orpheus. Orpheus fends off Metis, saving the SEES team from her attack. Igor would later mention that her awakening to the power of the Wild Card has bound her to a contract. The metamorphosis symbolizes a change in Aigis' psyche, and that her Journey is about to begin. Orpheus then serves as Aigis' initial Persona throughout the story. Aigis having inherited the protagonist's psyche and the Persona irritates a jealous Yukari.
Orpheus can also be obtained throughout the Wild Card shuffles after battles in The Answer.
"A Persona of another story. A Greek poet who tried to retrieve his wife from Hades, but she vanished when he looked back before reaching the surface."
—Persona 5 background
Orpheus appears as a DLC Persona, along with an enhanced version called "Orpheus Picaro," and can be bought at $2.99. Alongside Izanagi, Orpheus is free in the Japanese Deluxe Edition. Like Izanagi, he has a unique skill, "Cadenza," which heals all party members and increases their accuracy/agility, similar to the Fusion Spell in Persona 3, which requires Orpheus and Apsaras.
The female version of Orpheus is available as part of the game's Digital Deluxe Limited Edition and learns the skill Neo-Cadenza, which restores 50% of the party's health alongside increasing attack, defense, evasion and accuracy. 
While using cheats to get the full compendium in Persona 4, there are five extra slots in the compendium: 034, 0B4, 0B5, 02B, in the Fool Arcana including Izanagi-no-Okami. The slots 0B4 and 0B5 have a portrait of Orpheus but when summoned they appear as a Slime.
Compared to every other initial Personas in the Persona series, he has the worst affinities due to him having two weaknesses, without having any resistances to compensate.