The Breccia is a Troll crime syndicate in Ankh-Morpork, led by Chrysoprase the troll. It is much like any crime syndicate you might expect, thanks to the narrative force on the Disc, only it is run by trolls, so it is not a well-organized organized crime association. It is also quite violent.
In The Light Fantastic, Breccia (troll) is the name of an actual troll, who is introduced at about the same time as Chrysoprase (called Krysoprase at the time, spelling not being a trollish strong point). It's possible the crime syndicate is named after that Breccia.
There was a troll called Breccia working at Holy Wood during Moving Pictures who appeared to be a friend of Ginger. He wore woolen/cotton chain mail and complained that the pumice served at Borgle's still had the crust on and you couldn't taste the sand.
The civic association for trolls, the Silicon Anti-Defamation League, is sometimes rumored to be a front for the Breccia. There is little or no evidence to this, and Breccia itself is not well-organized, so it is unlikely that somebody will succeed in putting up a front, and Chrysoprase is widely known as a mobster, not a civic leader or businessman or head of charity organization. The Hollow Statue Imports Company established by Chalky the troll appears fairly typical of the Breccia's level of subtle thinking.
The Breccia sometimes meet in the Pork Futures Warehouse, so that in its cold atmosphere they can think or negotiate faster than usual.
The Breccia is a reference to the Roundworld's Mafia, a crime organization. The leaders of The Breccia are referred to as "tons", while the The Mafia refers to theirs as "dons". The name Breccia comes from a type of rock found on Roundworld, which is composed of many separate rocks held together by a natural cement. The analogy is that the various Trolls that compose the Breccia are all held together by a general unwillingness to stick to the letter, and often the spirit, of the law.
On Roundworld, Mafia godfather Joe Columbo forged a second career organising the Italian-American Anti-Defamation and Equal Rights campaign, to highlight and argue against this very point - while all the time creaming off charitable donations as part of his ongoing Mafia activities. Incredibly, many American politicians and TV opinion-formers supported Columbo to the hilt, while not stopping to reflect on the coincidence that the Italian-American anti-defamation league was headed by a man known to be a high-level mafioso godfather.... Columbo was eventually assassinated in 1971 on the orders of other Mafia bosses who were concerned about his high profile activities and lack of omerta.