In the modern western worldview, the afterlife is divided generally into two realms, heaven and hell. Heaven is where the "good" people go, and hell is where the "bad" people go. There are variations on this concept, but this is the general idea. Especially in Christian circles, heaven and hell are realms in which the soul resides permanently within this worldview based on either their beliefs or actions within this life.
It might surprise people to know that this was not necessarily the worldview of people in the first century, and this worldview is not what was taught in the New Testament. Nor does this worldview necessarily align with the thousands of testimonies from Near Death Experiencers around the world. This worldview emerged largely out of the Middle Ages and was heavily influenced by various theologians and writers until it emerged into the dichotomy we see today.
In the Greek, there are three words which are traditionally translated as hell, but only one of them might carry the traditional meaning. The first word we encounter in the Greek New Testament is Hades. This is actually the name of the Greek Olympian god and ruler of the Underworld. In the Greek worldview, the sky was ruled by Zeus, the Seas were ruled by Poseidon, and the Underworld was ruled by Hades. Over time, Hades' name became synonymous with the realm he ruled. The Underworld was a realm with various different regions and geographical features including several rivers, such as the Styx and the Leithe. The three main regions of the Underworld were the Elysian Fields where the virtuous dead went (in which ere also the Isles of the Blessed where the most heroic, righteous, and virtuous would eventually find themselves), the Fields of Asphodel where those who were not virtuous but also not wholly evil were consigned, and Tartaros (which incidentally is the only word in Greek which occurs in the New Testament that might correspond to the traditional concept of Hell, and occurs in 2 Peter 2:4) where monstrous souls who had committed grave offenses were consigned. This is described as the Abyss, the pit where the monstrous Titans who had castrated and murdered their father, Ouranos, were chained forever. This word, "abysson" is found in Revelation 20:3. It should be noted that in the New Testament, Tartaros and the Abyss are described as prisons for those Angels or Spiritual Beings who rebelled against God. They aren't described as prisons for human souls.
The final word which is traditionally translated as Hell from the Greek is "ge'enna" or "Gehenna." This word is a Hellenization of the Hebrew term "Gey-Hinnom." Most immediately, this referred to the Valley of Hinnom which was, at one time, a place of child sacrifice to Molech and then later a garbage dump as well as a place where the corpses of criminals and unclaimed bodies were dumped. Fires were kept going to incinerate the refuse, and as you can imagine, there were worms and maggot everywhere. That is the real-world image given by this word. But in Rabbinic literature in the first century and even up to this day in Jewish thought, Gehenna took on a spiritual meaning. It came to mean a place for those souls who had sinned or committed wrongdoing in this life to undergo correction as a kind of purification before passing on into the presence of God. In a way, the meaning of Gehenna was more synonymous with the Catholic concept of Purgatory than the modern concept of a permanent Hell. In Jewish thought, a soul could only remain in Gehenna for up to eleven months, no matter what. After the eleven months, they were allowed to move on. Gehenna was not a pleasant place to be, but the key idea here is that it was not permanent, nor was it ever seen as permanent.
Why then does the New Testament describe "Eternal Punishment"? Well, honestly, that depends on how you translate the words which are used in reference to this "punishment." First, the word used in reference to "punishment" in the afterlife is always "kolasis." This word doesn't mean vengeance or retribution. It means correction, checking the growth, or disciplinary action. Second, the word used which is translated as "eternal" in reference to "kolasis" is always "aionios." There are two words which can be translated as "Eternal" in Greek, but they have specifically different meanings. The first is "aidios," which means "forever, without end." This word is never applied to this disciplinary action in the afterlife in the New Testament. The second, as mentioned, is "aionios," which is a little more nuanced. It doesn't actually mean "without end." The meaning of "aionios" comes closer to the idea of "outside of time or undefined time." The gods in Greek mythology existed "aionios," but not necessarily "aidios." Aionios as a concept reflects a realm where time has no meaning. It's ageless. It could be five minutes, it could be a thousand years. It's a realm where all times are now, and past, present, and future don't apply. So, the disciplinary action being described as taking place in this Gehenna where the worm doesn't die and the fire isn't quenched isn't being described as being forever within a timeline, but taking place in a realm where time doesn't exist. And whether it's five minutes or eleven months is irrelevant except with the understanding that it's not permanent, and while the end of it is undefined, there will be an end to it.
Finally, among the many Near Death Experience testimonies are a number of what would be described as hellish experiences. These are much fewer than the heavenly encounters, but they do exist and they always leave those who experience it profoundly shaken and changed. What is important to note as common among these negative NDEs is that the person always seems to find themselves in a dark, nearly pitch black pit like region where they can't see hardly anything at all. They're always in some kind of torment, either emotional or seemingly being able to feel pain. There's usually some kind of negative beings present ready and waiting to inflict more excruciating pain and injury on the person. And finally, there's no sense of time. It is almost always described as it could have been minutes, it could have been thousands of years. From what I have read and heard, most of the people who encounter this were self-admittedly incredibly selfish and self-serving going into it and recognized that fact while they were experiencing it. They continuously reflected on how they lived their lives and the people they hurt either by commission or omission. What is incredibly important to note here is that many if not most came to the point where they cried out to God from this hellish place, having realized their mistakes, and God responded, usually by sending someone, usually Jesus Christ Himself or an angel of some kind, to retrieve them from there, heal them from their hellish experience, and bring them into a paradaisical realm where they would then experience the full presence and love of God unfiltered. They would then go through a life review, experiencing both how they had helped others and had hurt others from the perspective of the other person. Some then were given the choice of staying or returning, others were directly told they were being sent back.
Some may point out two specific passages which, in English translations, would seem to indicate that punishment is "forever" and that those cast into the lake of fire would be tormented "forever." These two passages are Matthew 25:41, 46 and Revelation 20:10. To sum up briefly, the first passage is the judgment of the "sheep" and the "goats," that is, those who were kind and compassionate to the least of these, and those who weren't. In Matthew 25:41 it reads, in the NABRE translation, "Then he will say to those on his left, 'Depart from me, you accursed, into the eternal fire prepared for the devil and his angels." And in 25:46, it says, "And these will go off to eternal punishment, but the righteous to eternal life." As I wrote previously, the word here used for "eternal" is not "aidios" but "aionios," or one of its cognates, in both instances. That is, outside of time, but not forever. Secondly, the word for punishment is, also as previously mentioned, "kolasis," which means "disciplinary action, correction," and in particular, "checking the growth of a plant." It does not mean vengeance or retribution.
In Revelation 20:10, in the NABRE it is very traditionally translated, "The Devil who had led them astray was thrown into the pool of fire and sulfur, where the beast and false prophet were. There they will be tormented day and night forever and ever." This sounds pretty straightforward... until you realize that the word "torment" is a mistranslation in this context, as potentially is "forever and ever." The word translated as "torment" is "basanizo," and it actually means "to investigate, put to the test, to examine closely, cross-question, interrogate." It can also have the meaning of "to question by torture," but the main concept of the word is the questioning, investigating, and examining, not the torture. The phrase in Greek translated as "forever and ever" is "eis tous aionas ton aionwn." Literally, it means, "into the ages of ages." This is an idiomatic way in Greek of expressing an undefined number of eons, that is, a very long, but indeterminate period of time or even outside of time. It implies that the end point is not known, but there may or may not be an endpont. It means that there is no certainty either way.
When applied to the idea of Gehenna, or when taken with the testimonies of NDEers who have had hellish experiences, the understanding of these original Greek words and phrases only reinforces the idea that this torment or hellish experience is not meant to be permanent and that release from it is not only possible, but intended once the person held within has come to their senses. It is undefined because that release is contingent on the person themselves coming to their senses and crying out to God.
Any time you see the word "hell" in a translation of the New Testament, it is rendering one of the words which I have just described, and the concepts which the original disciples and those who heard Jesus and first read the Apostles' letters were not what the modern word "hell" evokes. In their minds, at the very least, it was a temporary, disciplinary realm meant to purify the person in error and bring them to their senses, much like the NDEers describe from their own experiences. Those truly "hellish" realms like the Abyss, Tartaros, were intended for monstrous, powerful, and dangerous spiritual beings to keep them prisoner so they couldn't harm anyone. They were never intended for human souls, pieces and shreds of the Logos who is Himself born from the God, which were always intended to return to the God from whom they were born.