Once Upon A Time In Babylon
The first recorded mentionings of such a place are from Mesopotamia. One of the earliest texts we still have today is from the Epic of Gilgamesh which makes reference to Baal and the Underworld.
Later civilizations shared similar beliefs that most historians assume were inspired by each other, such as the Greek Tartarus, the Islam Jahannam -- to name just a few out of dozens. Plato for example was one of the heaviest influences on establishing hellenistic believes in the immortality of the soul and a Tartarus.
A Funny Thing Happened On The Way To Judaism
Abrahamic religions did not have a concept of hell or even an immortal soul, despite being surrounded by these believes. After Alexander the Great conquered much of the ancient world, the idea of Tartarus and the immortal soul may have entered Judaism. However, most of the mentionings of a place of torment are in Kabbalah or Apocrypha books and seem to indicate that it is only a place for fallen angels and not humans.
Christian Greek Scriptures teachings do not mention a place of eternal torment in the original Babylonian or even contemporary Greek sense. Neither is there a mentioning of an immortal soul. Jesus of Nazareth for example is known to have lived in Egypt for a while and was naturally familiar with Plato, yet none of these beliefs or ideas are ever mentioned in his teachings.
His later followers continued his lines of thought. One of the most prolific writers in the Christian Greek Scriptures, Paul of Tarsus, moved in philosopher circles and was familiar with the teachings of Plato and Socrates, as well as the Roman Tartarus as mentioned by the poet Virgil, yet he never adopted them either.
The only mentionings of a place for the dead (good or bad) in the bible has been the places Sheol and Gehenna, both commonly understood as meaning simply 'grave'. In the Greek translation of the Hebrew Bible, the Septuagint, the authors later used the Greek term Hades for the Hebrew Sheol, but with Jewish rather than Greek concepts in mind.
Christianity And Hell: The Comedy
Modern Christianity officially adopted the doctrine of 'hell' following the teachings of Augustine of Hippo beginning at around 400AD.
Augustine's time was one of philosophical turmoil, with literally hundreds of believes intermingling. Augustine himself as well as many of his friends -- among them one Jerome -- eventually both converted to Christianity, bringing with them their Greek philosophies and Platonist doctrines.
Heavily influenced by Manichaeism and Neo-Platonism (all of which teach the immortality of the soul) as well as each other, both Augustine and Jerome began on their works: Augustine laying the groundwork of what would become Catholic doctrine and Jerome (who is known to quote Virgil and Tartarus) translated the Septuagint from Greek to Latin, his work later known as the Vulgate translation.
Augustine and Jerome
But since both had already a basic belief in Platonist ideas, they both used the Septuagint translation of the word 'hell' in the Greek Tartarus concept -- as a place of eternal suffering for immortal souls, Infernus in Vulgate Latin.
And thus 'grave' became 'hell', changing the meaning of every single biblical scripture.
This mistranslation was made worse with Dante's Divine Comedy in 1320. The epic poem's imaginative vision of the afterlife is representative of the medieval worldview and in the following decades influenced art and doctrine. All modern-day images of 'hell' -- evil looking demons with wings and horns torturing naked bodies with pitchforks -- originate from the art that was inspired by the poem. It should also be noted that the guide through Dante's Inferno, is the above mentioned Roman poet Virgil -- acknowledging an amusing connection between Dante's Catholic hell and the Roman/Greek Tartarus.
The Vulgate is to this day the official Catholic translation, and all other translations into contemporary languages have used it as their base. As such the grave/hell switch was also translated into other languages, culminating in the King James version using the word 'hell'.
This discrepancy becomes obvious when looking at such scriptures as Acts 2:31 or Job 14:13 that describe Jesus going to 'hell' and Job desiring to go there as well. Other biblical translations that did not use the Vulgate or Greek influences as a base do not include this discrepancy. This has led to heavy arguments amongst Christian faiths over the veracity of translations.