The Black Sun, also known as the sonnenrad (sun wheel) in German, specifically comes from the floor of the north tower of Wewelsburg Castle, which was renovated by SS-leader Heinrich Himmler. The castle was a meeting place of only highest members of the SS, and Himmler considered it the axis mundi (center of the world) for their ideology.
The specific meaning of the symbol, if it even had one to Himmler, is unknown. There aren't even records of a name associated with this symbol. There is no suggestion that he called it the Black Sun; that term was associated with it afterward.
OriginsHimmler was highly interested in Germanic folklore and pagan belief and therefore appears to have adopted the symbol from similar historical shapes. While his Black Sun specifically has twelve arms, historical versions varied widely in the number of radiating spokes.
The historical versions are considered by many to be sun wheels, similar to sun crosses, which is why calling this symbol a sun comes easily to most. (However, one should note that the Wewelsburg symbol is made of green stone, not black.) The center of the Wewelsburg symbol also originally had a gold center to it, which is a common solar symbol.
Sun symbols commonly represent triumph, life and goodness, and sun symbols with central points to them often represent unity and centrality as well. All of these meanings fit well within Nazi ideology and worldview: the unity of a single race centered around a powerful party and leader triumphing over lesser, oppressive, evil races, embracing the fulfillment of life and goodness as defined by the Nazis.
Meaning of the Radiating SpokesThere are a variety of possible meanings in the design of the spokes. Germanic sun wheels commonly do have bent spokes. For Himmler, the bent nature was likely important because each spoke represented the Germanic sowilo rune of the Elder Futhark, which represented the sun. Himmler adopted a modern rune system which called the symbol sig and had it represent victory. His most known use of the sig rune is the insignia of the SS, which uses a double sig rune.
The pattern created by the crooked radiating spokes might also be interpreted as three overlaid swastikas. This interpretation has led some neo-Nazis to adopt the symbol, particularly in places where the display of swastikas are illegal.
Meaning of the Number TwelveThe chamber containing the Black Sun is known as the Obergruppenfuhrersaal, the Generals' Hall. Besides the Black Sun having twelve arms, this chamber also has twelve columns and twelve niches along the wall. There were twelve branches of the SS, so that may have been the relevance.
Other have advanced a comparison to the twelve knights of the round table. Himmler was a great fan of mythology and folklore, and two of the reading rooms within the castle were named Konig Artus (King Arthur) and Gral (Grail). As head of the SS, Himmler could potentially have also used such imagery in organizing the SS into twelve branches.
The number twelve also has relevance within Norse mythology. There are twelve Aesir gods, for example. Important groups of twelve can be found in other cultures as well, such as the twelve Olympic gods in Greek mythology and the twelve disciples who followed Jesus.
Beneath the Obergruppenfuhrersaal is another chamber that became known as the crypt or vault. It holds twelve seats against a wall surrounding a depression in the floor. The depression was meant to hold an eternal flame, a light emerging from darkness and rising up toward a swastika in the ceiling and then the Black Sun on the floor above.