"In Gehennom, only Moloch can hear you #pray." - Old Hacker aphorism...
Gehennom, taking its name from Gehenna (aka, the Hinnom valley outside Jerusalem, used in the scriptures as the metaphor for hell) is the "hell" in Nethack.
Generally speaking, it's not a really pleasant place to be. The legends from old ages tell that in previous versions of Nethack, the Hell was really Hell, and you couldn't survive without a ring of fire resistance. Now, I heard there was a shrewd shopkeeper, who previously had very powerful techno-magical skillz; He was called Izchak. He rewrote the Hell to be what is now known as Gehennom, a very different place indeed.
Gehennom in "vanilla" Nethack holds something more inconvinient in it than just fire and brimstone! In fact, it is not a place with fire and brimstone at all... It is a devilish maze. While most game players would find "fire and brimstone" version just an inconvinience, this one is really going to wreck their minds. In other words, perfect "Hell" material.
The Castle is the last level in the Dungeons of Doom; There are trapdoors in the Castle to get you in the Gehennom.
(Warning: Mild Spoilage Ahead)
Gehennom has 20 to 24 levels.
The bottom of the maze has the Inner Sanctum of Moloch, the place where the precious Amulet of Yendor is now kept. Getting there involves getting some artifacts from other places: The Bell of Opening, held by your Quest Nemesis in the Quest; The Candelabrum of Invocation, held by Vlad in his tower (a separate dungeon branch accessible through Gehennom - you can pray there); and, of course, the Book of the Dead, held by Rodney. You need to use those in correct place at correct time and correct order.
Rodney - such a cute and cuddly name for a big meanie called Wizard of Yendor - has his own Tower in Gehennom. Getting to the tower is somewhat of a challenge and the way construction of the tower may be perplexing for the uninitiated; Beware of the wizard's traps! Also, Rodney has this annoying tendency to not quit bugging you, and he certainly isn't thrilled about your idea to, ahem, aquire the Book.
Also of note are the domains of the demon lords. Lair of demon prince Asmodeus (who holds the gate to the deeper levels), the swampy home of Juiblex, the lair of Baalzebub, and the ghost town of Orcus.
Finally, the Valley of the Dead is the topmost level in Gehennom, and has a temple of Moloch.
Sources: Well, mostly off the top of my head (not that I've ever been to Gehennom outside Wizard Mode, but I read the spoilers couple of times before =)... Dylan O'Donnell's Nethack 3.3 Spoilers helped me to Remember.