Actually, it was the Sicilians, not Italians. The mafia is an ancient way of life adhered to generally in Sicily for at least 1500 years. The adherent to mafia is known as the mafioso. The code of conduct for the mafioso is known as omerta. It is sort of a poor man's chivalry that stresses vengeance and eye-for-an-eye justice. Sicily was frequently invaded in ancient times and the inhabitants developed mafia as a way of resisting these invaders. When Sicilians later immigrated to other places they retained mafia and continued to practice it. Outsiders tend to see mafia as a type of criminal conspiracy, but actually the Sicilians use it for everything, both lawful businesses and criminal activities.
The advantage of following omerta in crime is that it is first and foremost a personal code that requires no courts or authority, so it can operate as a method of justice without a central authority. In criminal activities, this is an advantage because such activities lie outside the courts. For example, if you buy dope and your dealer rips you off, you have no recourse. If you call the police, they will just arrest YOU, not give you justice (this actually happened, btw, some woman called the cops to complain about her dealer ripping her off). For those living within mafia, they always get justice. The advantage of this system compared to undisciplined criminals who have no code should be obvious.
There is a similar system local to Naples called the carbonari, but this was never developed to the extent of the mafia. The Carbonari had the same origin as the Mafia, resistance to foreign invaders.