Its name is German for over the woods, as a play on Transylvania, which is Latin for across the woods. In fact, this name was actually used for Transylvania in some documents from the 13th century. The region is based less on the real Eastern Europe, and more on the Hammer Horror stereotype of the area. In keeping with the Discworld's affinity for narrative, Überwald's climate and conditions contrive to fulfil human expectations: for example, Überwaldian lightning strikes whenever someone makes a particularly forceful pronouncement. In The Truth this phenomenon is referred to as "psychotropic weather."
The spelling of the German-language word is certainly "Überwald". The usage in some of the books is uneven, but the later narratives use "Uberwald" exclusively. In Carpe Jugulum, Pratchett writes:
The region was previously united under the rule of the Unholy Empire (a play on the Holy Roman Empire), which had a two-headed bat as its symbol (a play on the double headed eagle). The Empire has long since collapsed leaving the area fragmented, chaotic, and under the rule of lore, not law (the two words pun when spoken with certain British accents). Although Überwald has a large human population, they play a secondary role in the region's history. It is ruled by dwarfs, vampires, and werewolves; while there are a few human barons, they tend to be uninterested in politics, preferring experimental surgery and Meddling In Things Man Was Not Meant To Wot Of with the help of their Igors.
Überwald's economy is apparently based on mining. Though precious metals are plentiful, the most crucial mineral resource is fat, which is believed to have been deposited by a fifth great elephant which dislodged itself from the back of Great A'Tuin and crashed into the ground around Überwald. Boiling fat rising to the surface is the reason for the country's many hot springs.
Überwald effectively comprises two utterly distinct societies; the dwarfs, who exist below in their cavernous cities and tunnels, and everybody else, who live above. By tradition, the laws of the surface people do not apply underground, and vice versa. Überwaldian dwarfs are far more hidebound and traditional than their cousins near the Sto Plains, which has led to a certain culture clash between the two. Überwald is the centre of Dwarfish history and politics; the Low King, the final arbiter of Dwarfish law, has his seat of power in the underground Überwald city of Schmaltzberg.
From the Diet of Bugs (a play on the Diet of Worms) onwards garlic and silver were considered contraband across Überwald until the events of The Fifth Elephant; the undead simply promised they would not be needed. Apparently this system left something to be desired.
There are innumerable castles scattered around the cliffs and crags (You can't move for remote castles ~Lu-Tze) of Überwald so it would be impossible to name them all; some of the more notable ones are listed here:
Carpe Jugulum dealt with a family of vampires from Überwald attempting to take over Lancre. The novel The Fifth Elephant was set mostly in Überwald, and details a power-struggle between the dwarfs, with involvement by vampires and werewolves.
In the book The Amazing Maurice and His Educated Rodents, the main town (Bad Blintz) is in Überwald.
In Discworld Noir two characters, Carlotta von Überwald and "The Count" are part of the Überwald aristocracy, though for the duration of the game live in Ankh-Morpork.