- "Beautiful, isn't it ? Such raw unbridled power. It destroyed the Thule Civilization; but where they failed, we will succeed. I have the technology to control it. And our first demonstration will be the city of Isenstadt. After that, I will destroy everything that stands in my way - the world will fall on it knees before the Third Reich. A shame you won't get to see the swastika flying proudly over Washington D.C."
- ―Deathshead revealing his plot to B.J. Blazkowicz.[src]
The Black Sun Dimension (German: Nachtsonne-Dimension) is a dimension parallel to Earth's dimension. It is very unstable, drawing bits and debris and even life forms into the central dominating feature, the Black Sun itself. The Nazis stumbled onto this destructive dimension, seemingly due to locating the first Thule Medallion. They began to develop machines to harness the dimension's power. It resembles the Veil, albeit with a Black Sun where the normal sun might be; this sun can be seen to draw matter into it, and causes the swirling trails of wreckage spiraling into the sky which are visible in the Veil. Unlike the Veil, it does not bear any relationship to Earth's dimension. The only parts seen being drifting platforms suspended over a black void.
The Thule apparently constructed buildings of some kind inside the Black Sun Dimension, though only their ruins are left, and also built a huge mechanical structure to harness the power of the Black Sun, which ultimately led to their destruction; this is the same device which the Nazis plan to use to power the Zeppelin's doomsday weapon. Seemingly the Queen Geist came from the Black Sun Dimension, since she is summoned due to the Veil being torn and is able to escape being pulled in by the Black Sun itself.
Directly entering it without access to a Thule Medallion or some other protective measure mutates humans into deformed monsters, which are stronger than they originally were, but lose their minds. It is not precisely clear how the blindfolded soldiers in "Hospital" or Deathshead and his minions at the end of Wolfenstein avoided this fate, but at one point a scientist mentions that it is necessary to "tune the harmonic frequencies" of a portal before humans can pass through unaffected.
The Black Sun Dimension appears after defeating the Altered, the Queen Geist, and finally at the end of the mission "Zeppelin." The first two times BJ is pulled into a rift in the Veil leading straight to the Black Sun Dimension, while the final time he walks through the Thule Portal to take on Hans Grosse and destroy the Thule device once and for all, preventing the Nazis from ever using it again.
The Black Sun is the source of energy of the Veil-powered weapons. The Veil is the barrier and draws its energy from the Black Sun Dimension, making the Black Sun the source of energy. It is this dimension that will fuel the Nazis' doomsday weapon that is supposed to fire on Isenstadt from the zeppelin ever-present in the sky. The weapon is so destructive, that all soldiers are to be ordered out of Isenstadt prior to its firing, else they will be "consumed by the power of the Black Sun". The destruction of the Midtown of the Isenstadt is persumably caused by the zepplin hovering above it.
Behind the scenes
The Black Sun (Schwarze Sonne) otherwise known as the Sunwheel (Sonnenrad) is a concept in real-life Neo-Nazi occultism and the symbol of the Black Sun, a many-armed Sunwheel, was present on the floor of a room in the inspiration for Castle Wolfenstein, Castle Wewelsburg. While there are several sets of beliefs incorporating the Black Sun, the game uses one which claimed it to be an ancient power source which had once given strength to a pre-human race of giants living in the far north, called the Thule or Hyperboreans. This dead star was believed to have the power to regenerate the Aryan race, supposedly descended from the Thule, to their former state.