To provide some context, Puzo's mafia is one that sees itself having grown out of the numerous conquests of Sicily. Untrustworthy of and oppressed by formal governments, Sicilians took to a sort of shadow government operating on a code of omerta (silence) that could in effect control the island.

I forget the extent to which Puzo agrees with this, but it's a theme that runs through most of his books (all of the ones I've read, anyway).

I'm only halfway through Five Families by Raab but based on that and my general understanding of the mafia, the American mob abandoned any pretenses fairly early on and was just about making money. They didn't take orders from Sicily and connections weakened early on. But I'll leave it to someone else to directly answer your question.

edit: I'd just add that the whole Sicilian community participates in the mafia world of Puzo, that's how the shadow government subverts the real government. If nobody ever talks to the police, asks anything of the government, and solves all of their problem with an alternative source of violence (government's are governments because they have a monopoly on violence), then it's sort of a checkmate on being conquered by more powerful invaders. This would explain why Corleone occupies the position he does - these people see themselves not as Americans, but as Sicilians, and Corleone is king.

Oooh! Oooh! Oooh! I've been waiting so long to answer a question like this because a year or two ago I was deeply into research onto the Mafia for an academic project.

I highly recommend you read the books of Diego Gambetta, who is a Cambridge sociologist who extensively studies organized crime and trust problems. His contention is that the core activity of the Mafia in Sicily was protection racketeering. Furthermore, the Mafia is NOT a product of Sicily being invaded all the time since antiquity (every culture has experienced frequents invasions - why don't Belgians have an infamous mafia?). The Mafia arose in the 19th century and is a consequence of capitalism and the Sicilian state's inability to properly police it.

To provide some context: In the 19th century Sicily dismantled its old feudal state and became a modern market economy. This process was further accelerated when Garibaldi invaded the island and annexed it for Italy. The feudal barons who once ruled the land now handed over the responsibility of maintaining law and order to the new democratic state. Except this new state was riddled with corruption and incompetence (I think a similar parallel might be Russia during the 90s). There were hardly any cops at all on the island (a few hundred at most). The state was terrible at keeping the peace and enforcing contracts, so the people turned to extralegal arbitrators. Namely gangsters. This I think is what happens when a state fails to organize and train a police for made up of decent people: The people were forced to hire the services of those who were already proficient in violence, and this usually meant ex-soldiers or violent criminals.

This an illustration that Gambetta provides in his book of Mafia protection in action: Say a butcher wants to sell some meat to a supermarket, tax-free. Because this is essentially a black market deal, neither the butcher nor the grocer can sue the other in court in the case of foul play. What happens if the butcher sell some bad meat? What happens if the grocer doesn't pay the butcher? Each party is tempted to cheat the other and the mutual distrust may prevent them from making a profitable transaction. To prevent cheating, the two parties will invite the local mafioso to oversee the deal. The mafioso promises he will punish either of them if they cheat the other (by a sound beating, I should think). Because the mafioso is so feared for his violence, self-discipline, and uncompromising nature, neither party dares cheat the other and the transaction occurs smoothly. In exchange for his oversight, the mafioso takes a cut of the sale. Or maybe he'll ask for some favors in the future (and his clients better please him if they know what's good for them).

Mafiosi also protect property from thieves and vandals. If you're paying protection money to a mafioso, then if ever someone dare messes with your property or your family, then you can expect your mafioso to beat the shit out of the miscreant. In New York, I am told that Little Italy during the 80s was such a safe neighborhood that grannies could safely walk around at night. Criminals knew that the Mafia didn't fuck around like the courts did, what with the latter's obsession with "due process" and "reasonable punishment".

So as you've gleaned, the core service that the Mafia provides is protection. Protection from cheats, thieves, assailants, etc. They may ask for money or for favors in return. This is what that guy in the opening scene of The Godfather was asking: protection (or retribution, more appropriately) for his daughter, whom the courts failed. If only those two thugs had known that the girl's father was connected!

Now the next question you have to ask is why are mafioso treated with such respect, their bosses treated pretty much like medieval kings? The answer is that the demand for the don's (will call the boss of a clan a don for fun) protection is very high. Mafia activity in Sicily was concentrated in the cities like Palermo and in the small citrus orchards around it. In these areas there was an intense concentration of economic agents (merchants and plantation owners), which meant that a mob boss had at least dozens of potential clients within his territory (It's critical to note that mobsters violently chase rival mobsters out of their territory. They have a monopoly on the protection business within their territory). This meant that a boss could pick and choose who gets his protection and who is left to the wolves, so people bent over and kissed ass to curry favor. The situation in the eastern half of the island was different: These areas were more sparsely populated, and the countryside estates tended to be really large, requiring the full-time protection of a guardian. The people who guarded these large estates were more like employees than lords. They didn't have the kind of bargaining power that the mafiosi in the west had.

You can see here that the power and respect a mafia boss has is not to different from that of a feudal king. A feudal king ruled over thousands of subjects and could grant disproportionate security and privileges to people he favored, and so his subjects would kiss his ass constantly to get on his good side.

Mafiosi also meddle in the democratic process. Mafiosi demand strict obedience from the people in their spheres of influence, and thus can easily persuade their people to vote for a certain political candidate. This is a quote from the autobiography of the Sicilian mobster, Antonino Calderone:

Politicians have always sought us out because we can provide votes. [...] between friends and family, each man of honor can muster up forty to fifty other people. There are between 1,500 and 2,000 men of honor in Palermo province. Multiply that by fifty and you get a nice package of 75,000 to 100,000 votes to go to friendly parties and candidates.

That's how things work in Sicily. I don't know how vulnerable American democracy is the mob, but I imagine if a politician needs to do some crooked deal and needs protection, he might consult his local don. I don't know as much about how the Mafia in America works. Prof Gambetta's work focused on the Sicilian Mafia (being Italian himself it was easier for him), and the American Mafia cannot be the same because America is a very different environment. Practically every book I read on the American Mafia focuses on personalities and specific crimes (this guy shot that guy and stole from that other guy then got whacked himself badabing fuggedaboutit, etc.), with no socio-economic analysis.

Just to add to this, the story has this happening specifically at the don's daughters wedding, how accurate is this?

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