Prometheus was one of the Titans to sided with Zeus and his siblings in the great war against the rest of the Titans, the original rulers of the world. When Zeus won the war and banished Prometheus' brethren to Tartarus for eternity, Prometheus and his brother Epimethius were given the task of populating the earth with creations.
Epimetheus, who created the beasts of the world, gave his creations all of the gifts that could be bestowed, leaving Prometheus with nothing to give to Humanity. To compensate, Prometheus stole fire from Mount Olympus, incurring Zeus' wrath. However, it wasn't until he taught mankind how to trick the gods that he was given his ultimate punishment. Chained to a rock for all time, his liver was eaten every day by a great eagle sent by Zeus. Immortal, he could never die and his liver would regrow. And so he suffered, until the Greek hero Heracles freed him from his torment during the course of his famous Twelve Labors.
"A Titan of Greek lore. He was very intelligent; his name means "forethought." He stole fire from Zeus and gave it to mankind. Zeus chained him to a rock as punishment and set an eagle to eat his liver every day. He was kept there until freed by Hercules."
Prometheus is a boss in the Challenge Quest, Defeat Demon In Ginza, where he has been attempting to give humans fire to strengthen them. All fail and disappear upon the flame passing through until he fights Nanashi to see if he is worthy. Upon defeat he realizes he is not only worthy but already wields the flame, deciding to leave since someone has been proven to wield such power.
The design of Prometheus as a Persona has large rocks attached to his bodies. These rocks represent the rock which trapped Prometheus in his originating lore. Before Kazuma Kaneko designed Prometheus for the Persona game, the rocks were more irregular. However, as Kaneko's Persona designs were based upon fashion, those rocks were alternated to resemble the gears in vanguard fashion. The red lines on the rocks represent the energy or fire stolen by Prometheus. On a side note, these concepts of the rocks and red lines reappear in the Obelisk of Shin Megami Tensei III: Nocturne.
"The Greek Titan created mankind from clay. He later stole fire from Olympus and, in turn, gave it to mankind against Zeus's will. His often synonymous with fire and "divine knowledge"."
—Persona 5 background
Prometheus is the ultimate Persona of Futaba Sakura. It resembles a large, floating orb that has a series of rainbow linings around it, forming a large grinning face, and is surrounded by flames. It gains the ability to detect rare items from enemies along with the abilities it inherited from Necronomicon. The animations during which Futaba uses Necronomicon, even the interior details, also remain.
"A titan in Greek mythology, his name means "foresee". The Titans were the race of giants who ruled the world before the great Olympian gods. Prometheus is well known for stealing fire from the gods and giving it to mankind."