Hell is, according to many religious beliefs about the afterlife, a place of torment, of great weeping and gnashing of teeth. On any conception, it is a place of eternal separation from God and the pleasures of Heaven. The English word 'hell' comes from Old English 'Hel', meaning underworld.
Hell, as it exists in the Western popular imagination, has its origins in Christianity. Judaism, at least initially, believed in Sheol, a shadowy existence to which all were sent indiscriminately. Sheol may have been little more than a poetic metaphor for the death, not really an afterlife at all: see for example Sirach. In any case, the afterlife was much less important in ancient Judaism than it is for many Christian groups today; indeed, the same can be said for modern Judaism as well.
The Hebrew 'Sheol' was translated in the Septuagint as 'Hades', the name for the underworld in Greek mythology. The New Testament uses this word, but it also uses the word 'Gehenna', from the valley of Ge-Hinnom, a valley near Jerusalem in which in ancient times garbage was burned. The early Christian teaching was that the damned would be burnt in the valley just as the garbage was. (It is ironic to note that the valley of Ge-Hinnom is today, far from being a garbage dump, a public park.) Punishment for the damned and reward for the saved is a constant theme of early Christianity.
Another source for the modern idea of 'Hell' is the Greek Tartarus, a fiery placed in which evildoers where punished. Tartarus formed part of Hades in Greek mythology, but Hades also included the Elysian fields, a place for the reward of heroes (though some sources have the Elysian fields, not in the underworld, but as islands in the west), whilst most spent a shadowy existence wandering the asphodels (a flower, most likely Narcissus poeticus) fields. Like most ancient (pre-Christian) religions, the underworld was not viewed as negatively as it is in Christianity.
Obviously, we need an erudite account from someone who has studied the relevant theology.
According to popular imagery connected to the Christian mythos Hell is a place ruled by the Devil, or Satan, who is a person who carries a pitchfork and has flaming red skin, horns on his head, and a long thin tail with a diamond shaped barb on it. Hell is a place underground, with fires and molten rock. Demons, looking much like the Devil, eternally torment the souls of the dead. Christian theologians (or at least those who believe in the traditional Christian idea of Hell) reject this view: the popular image of the devil has no biblical basis (it may be a Christian corruption of the god Pan), and rather than demons punishing humans, demons themselves are punished in Hell along with the humans led astray by them.
Most Christian groups teach that Hell is eternal. Some however believe that Hell is only temporary, and that souls in hell cease to exist after serving their time there; this belief is called annihilationism. Others believe that after serving their time in hell souls are reconciled to God and admitted to heaven; this belief is called universalism.
Some Buddhists believe in several Hells, which are places of punishment for evildoers. Those with sufficently bad karma are reincarnated there, where they stay until their bad karma has been spent, whereupon they are reincarnated as humans.
See also damnation