The term "messiah" comes from the Hebrew Bible and is properly romanized as "mashiach." Its literal meaning--anointed one--refers to its initial context as a purification ritual for Hebrew kings using oils.
The earliest idea of the prophesied savior figure, as the term would later be synonymous with, comes from Zoroastrianism and the Saoshyant, who was said to return to Earth in a thousand years (from a date of approximately 1000 BC) to finally give the edge to Ahura Mazda, god of light and truth, who waged a battle with the demon of dark and falsehood, Angra Mainyu. The Saoshyant is a son of their great prophet Zarathustra, whose semen would lie in a lake and impregnate a virgin woman once the time of the Saoshyant's conception was determined. That no Saoshyant ever appeared is one factor that lead to the downfall of Zoroastrianism in the Middle East.
During and after the Hebrews' Babylonian exile, they would encounter this myth and also the Persian king Cyrus the Great, who allowed them the freedom to return to Israel. For this, they called him Messiah, and the prophecy of the Jewish savior entered their religion.
In Christianity, this prophecy came to fruition in the form of Jesus Christ, who was said to be born of the virgin Mary and was sacrificed by God to free mankind from the vices of sin.
Today, the idea of the messiah is perhaps most encountered in the form of false messiahs and cult leaders who claim special knowledge of God or to be incarnations of Jesus and other figures, yet lead their followers to tragedy. Once such famous example in the United States is the Branch Davidian leader David Koresh who was killed along with his followers in Waco, Texas in 1993.
In Persona 3
Messiah is one of the most powerful personae in Persona 3. He is from the Judgement Arcana and is only available late in the game due to his high level. He can be obtained by fusing Orpheus and Thanatos in the Velvet Room. Like Orpheus, Messiah somewhat resembles the main character, since he is considered his ultimate persona.