Used by Sicilian gangs, it is now a separate branch of organized crime. It's meaning is literally, "This thing of ours". It goes back hundreds of years, when the Mafia was invented to protect Sicilian families from maurauding gangs and conquerers.
Lucy Luciano was known for bringing La Cosa Nostra to the United States.
Literally "Our case" or "Our business", Italian term. Especially used a lot in reference to the mafia. Also a synonym for mafia. Both sort of forbidden words, not used in Godfather 1.
The Cosa Nostra are fighting the Colombians.