Is Hell in the Bible?
The answer is more complicated than you might think. In many Bibles, two different words are translated as Hell. The first is Hades, which refers to the Greek underworld, or the place of the dead. The other is Gehenna, which was an actual physical place. The NRSV translation of the Bible is intentional about separating the two. Hades is left as Hades, and Gehenna is translated as Hell. Each word though, provides a richness and nuance which helps us to understand our plight as human beings, as well as the redemptive work of Jesus Christ.
What is Hell Like in the Bible?
The most vivid description of Hell comes in Luke 16:19-31, the story of the Rich Man and Lazarus. In this story, Jesus describes a rich man who ignored a destitute beggar named Lazarus. When each of them died, Lazarus was brought by angels to be with Abraham, and the rich man went to Hades. There he was suffering from torment and flames. This is the closest description we get in the Bible to the popular idea of Hell as a place of fire and brimstone for unrepentant sinners.
In the places where the New Testament refers to Gehenna, it is usually described as a place where sinners go to, sometimes with the imagery of where the worm doesn't die, and the fire doesn't go out (Mark 9:48)
Gehenna - Literal Hell
The question becomes more complicated when you realize that Gehenna was a literal place, and a pretty nasty one at that. The original place was the Valley of Ben Hinnom where ancient pagans would sacrifice their children to the god Molech. This practice even continued into the days of Israel's prophets (Jeremiah 7:31), so much so that the valley was cursed by the prophet Jeremiah (Jeremiah 19:2-6) By Jesus' time the place may have become a garbage dump. It only makes sense that people would not want to be associated with such a place, so they used it for their trash.
Some sources claim that fires were burning constantly to take care of the odor, but I have another theory. Organic waste needs to be managed very carefully. In the presence of oxygen it will break down nicely. Without oxygen, the process can turn anaeorbic, which will produce methane as a by-product. Methane is combustible, and can spontaneously ignite if present in sufficient concentration. This may be the source of Jesus' description of the worm never dying and the fire never going out in Mark 9:48.
But this understanding also makes the references to Gehenna (Hell) even more poignant. This was a real place where people had done unspeakable things. The closest thing we can refer to in our own society is Auschwitz. So when Jesus said that calling someone, "You fool," would make you subject to the fires of Gehenna (Matthew 5:22) it was as much a warning about the moral path they were on. The end of that path was a very depraved one.
Hell vs. Hades
In it's purest sense, Hades was the place of departed spirits - nothing more. It was a way of describing death. Later Greek mythology established various places such as Tartarus, Elesium, and The Asphodal Meadows for the wicked, righteous, and indifferent souls. But at its core, Hades is the place of the dead, and the trip in is one-way. Souls enter, but they do not leave.
You may be wondering why such a word would even exist in the Bible. The answer is even more complicated, because a very similar concept appears in the Old Testament. If you were to read the Old Testament in its entirety, you would not find a distinction of Heaven or Hell as the fate of people when they die. Instead there was a concept called Sheol, which like Hades, was the place of departed spirits. During the time of the patriarchs, even Jacob assumed that once he died, he would end up in Sheol (Genesis 37:34-36).
Hades for the Early Church Fathers
Driven by both Scripture and reason, many Early Church Fathers came to understand death / Hades not as a thing of itself, but rather the absence of a thing. God was obviously the source of life, so death, by its very definition, represents an absence of God. Gregory of Nyssa, in his Address on Religious Instruction, argues for this understanding in his chapter, "The Nature of Evil and the Fall of Man." In it, Gregory describes how many things, such as darkness, are opposed to their opposites, in this case light, but do not exist in their own right. Darkness is not an actual thing, it is the absence of a thing: light. So for Gregory and many other of his contemporaries, the work of Christ's redemption was to rescue humans from Death / Hades / a state of non-being.
What did Christ do to Hell / Hades?
To me, this rich understanding of Hell makes Christ's death and resurrection all the more powerful. Briefly, by being fully human, Jesus was able to experience death, or Hades, or Sheol, or whatever you wish to call it. (These words are often used when people are trying to describe the indescribable.) But since Jesus is also fully God, he was able to negate death from within. Gregory of Nyssa, in Catechetical Oration, 26, said, "When death came into contact with life, darkness with light, corruption with incorruption, the worse of these things disappeared into a state of non-existence."
To use some more poetical imagery, it was as if Christ was a soldier leading an attack on Hell itself - the incarnation being even more cunning than the Trojan Horse. Hell / Hades could not withstand the mere presence of the source of all life, and its very existence crumbled before Him. The gate, which once only permitted souls to enter, but not leave, was now damaged beyond all recognition, allowing not only Christ to return to the land of the living, but everyone else trapped within.
A wholistic, Biblical concept of Hell goes beyond the simple definition of a place for wicked people to be tormented. Over the centuries during which the Bible was composed, the concept grew from Sheol, a simple dreary place for departed spirits, to the multi-faceted understanding of Hades, and the very real place of Gehenna. But coming to understand it as a place where human beings eventually are subjected to (everyone dies), we can understand Christ's redemption in a much richer, nuanced way. He entered into the very place where all humans are destined (death). As perfect God and perfect man he could both experience death and negate it from within. The powers of death / Hell / Hades are conquered and rendered impotent at the very presence of the God-Man, opening up for human beings the way of resurrection and eternal life.