Literally "Our Thing". This is the name usually used by those who are actually in the Mafia or Mob. Organized crime groups of Sicilian extraction.
The origins of the group are lost in history but there are two main theories as to their origin. One is that they were resistance groups to the invasion of Arab and Norman forces in the 9th and 10th centuries. The other is that they evolved out of groups of toughs paid by local nobility to protect their estates from other bandits.
Whatever their origin they largely controlled Sicily by the 19th century. With immigration to the United States by Italians so did the "honored society". At first they were mainly centered in the port of New Orleans, but around the turn of the 20th century immigration shifted and more went to New York.
The tradition of black hand extortion arrived in the New World with these thugs exploiting their fellow immigrants, and some became wealthy and powerful off of this oppression. But it was the prohibition of alcohol starting in 1919 that really made the Mafia organized. It and a few other ethnicity-based organized crime groups grew very powerful by providing illegal liquor as well as other traditional vices.
Their power remained intact long after the end of prohibition due to their strength and making certain neighborhoods safe. By protecting a few neighborhoods around their headquarters they gained the loyalty of the people living there and were free to continue with their businesses of robbery, murder, extortion, prostitution, drug dealing, and bookmaking in all other parts of the cities. This also spawned the false view that the Mafiosi were benevolent criminals in the mold of The Godfather. Make no mistake, they were kind to some, but so are all tyrants, else they would have no power base to rule from.
The Sicilian crime families remained powerful through the 1970s, but started to decline in power due to a lack of the previous loyalty to the code of Omerta, self-destructive behavior, and increasing prosecution under the RICO Act. Currently, the Italian mob is a shadow of its former self. More and more various Colombian, Mexican, Chinese, and Russian groups are taking their place.