The concept of "Hellfire" is a Christianization of pagan and Greek philosophies.
While it's a common historical talking point that the Catholic Church invented the vivid, fiery tortures of Hell, the concept of eternal burning actually predates Christianity by centuries.
Instead of inventing it, early Western Christianity essentially merged pagan language with Greek philosophy to create the concept we know today.
Where it actually came from:
• Ancient Civilizations: The oldest depictions of hellish "pits of fire" for bad souls originate in Ancient Egyptian texts (like the Book of the Dead) and Babylonian mythology.
• The Language: The word "Hell" is actually a Germanic, pagan word (Hel or Helle) that originally referred to a cold, misty underworld in Norse and Anglo-Saxon mythology. When early Christian scholars translated the Greek New Testament's Gehenna tou pyros ("the Gehenna of fire") into Old English, they smashed the pagan word together with fire to coin hellefȳr (hellfire).
• The Philosophy: Early Judaism generally focused on Sheol—a neutral, shadowy grave where everyone went. However, as Christianity grew in the Greco-Roman world, early theologians blended scripture with Platonism. Plato's ideas popularized the concept that the human soul is inherently immortal and must face post-mortem retribution.
What the Church actually did:
Edit: I've updated the relevance of Gehenna
By marrying the Hebrew imagery of Gehenna (a real-world valley outside Jerusalem that had an abhorrent history associated with pagan ritual child sacrifice) with the Greek concept of an indestructible, immortal soul, the early Church formalized the doctrine of eternal conscious torment.
By the 5th century, theologians like Saint Augustine locked this into official church dogma, turning a collection of vivid ancient metaphors into a highly codified system of societal control.
TL;DR: The blueprint for a fiery afterlife belongs to ancient pagan religions, the word "Hell" belongs to Norse/Germanic pagans, and the idea of an immortal soul being tortured forever comes from Greek philosophy. The early Western Church just took those pieces, fused them together, and aggressively branded it as "hellfire."