This is a very complex question that has puzzled historians, politicians and economists for decades now.

As others have said, Sicily was once among the wealthiest regions in Italy until 200 years ago. Equally, Naples was considered a world capital until 19th Century, together with Rome and Paris.

There is a constellation of reasons why the South of Italy has lost its advantage compared to the Northern part of the Country and it is now among the less developed areas in Europe, no matter how many billions of Euro the Central Government and the European Union pump every year in the attempt to revive the South of Italy’s economy.

In particular:

1. Times have changed and culturally Southern Italians have been unable to adapt: the southern part of Italy was an agriculture-based Economy for centuries. In the last 150 years agriculture has lost its dominance over the Economy: first in favour of the Mechanical Industries (the Industrial Revolution sparkled by the Brits), secondly in favour of the Services Industries. Southern Italy missed completely both of these economic revolutions.

These huge missed opportunities had three main consequences that you can still notice today:

• Structural lack of social mobility: children end up doing the same jobs of their parents. This is (unfortunately) a common trait of all Italians (North and South alike), but according to the statistics it is particularly exacerbated in the South of Italy (and they love it like this). Given this premise, it is extremely difficult for a lower-middle class Southern Italian to climb the social ladder. This is not an accidental by-product of the social contract in force: through a thousands of written and unwritten rules, the system achieved this by design. The South of Italy’s upper / ruling classes have purposely done everything (legal and illegal) in order to prevent including the middle and lower classes in the modernisation of the Country. In the long term, this destroyed the South of Italy middle class, leaving an ever increasing divide between the ultra-rich, watertight, rent-seeking upper/ruling classes and the vast majority of the lower classes.
• Few risk takers: there is a very low entrepreneurial attitude among Southern Italians (especially the middle class): most of «the best and the brightest» (and there are many, very smart, hard-working and able) end up in the Government bureaucratic machine not unlike what happens in Japan. Not unlike Japan, this is done by design. This (and this only) is considered — work-wise — a “success” in the South of Italy, with the result that thousands and thousands of smart, young and very able Southern Italians of every possible root apply every year for any available vacancy within the bureaucratic machine (including magistrates, state administrative jobs, notaries, law clerks, etc.). Jobs are simply “requested” by the base as a sort of “welfare” and award for the smart, hard-working & able, and not the natural by-product of a healthy local economy. Nowhere is taught to the younger generations that entrepreneurship is a valid option for the smart and able;
• No highly specialised service economy: as mentioned above, the service economy in the South of Italy has translated into bureaucratic jobs manufactured by the Italian central government for the sole purpose of giving jobs to the people in the (lame) attempt to revive the local economy. As a consequence, this has created enormous State-owned conglomerates with zero public usefulness and has instated an iron-clad mentality into people that the safest / best jobs anyone could find are those with the State (i.e. you cannot be fired and once you get the job, you are set for life, you will get a mortgage, you can get sick for years and never get fired, etc.). The Central Government originally fuelled this attitude by hiring more than 180k people from South of Italy in their internal bureaucracy just in the few years after the WWII. Historically, there was a huge inflow of Southern Italians all over the bureaucratic machine at all levels and, in a critical time of reconstruction of the Country, this destroyed the need for Southern Italians (or at least their active, educated middle class) to approach the real market and create jobs that were actually needed and not «manufactured» for political purposes. To date, it is estimated that in the South of Italy, 1/3 of the active population is unemployed, 1/3 works in private companies and 1/3 works for the State or State-owned companies. This means that half of the working population works for the State (with higher than average salaries and future-proof job protections, compounded by ridiculously low level of productivity). Things are slightly improving now, but in the meantime the generation of our parents was lost forever.

2. Brain drain: for generations, the extreme poverty and structural lack of social mobility forced millions of bright, risk-taker, Southern Italians to leave the Country, in most cases in favour of Southern and Northern America. This prevented a cultural change at home, because the incumbent, upper-class, people with the «old» mindset had firmly the reins of the political, administrative, legal, judicial and, most importantly, financial machine for generations and no change of mindset was conceivable to come from the system’s insiders (who traditionally have been silently (but immensely) profiting from the status quo for generations). In recent years, the emigration abroad was reduced thanks to substantial subsidies by the central government, while it increased the internal migration from southern regions to the north of the Country (in 2015 alone, 138k Southern Italians under 30 years old moved to the Northern part of the Country in the attempt to find a job).

3. Organised Crime: in the last 150 years a small part of Southern Italians have developed a net of strong, violent and highly profitable criminal organisations with foothold in the social and political system of almost every city in the Region. This system sucked resources both from the (already lagging behind) economy and also from the Central Government investment in the infrastructure & health-care system (both among the most corrupted in Europe). These criminal organisations have been able to command the political agenda for decades, and, not unlike what happened in certain South American States, have been willing to corrupt and if necessary even kill magistrates, policemen and politicians in order to escape justice and to deadlock any attempt by the central government to repress the crimes and reform the legal grey-areas that allow criminality to thrive (e.g. legalization of marijuana).

4. Higher rates of school abandonment: for decades, Southern Italy has seen higher rates of kids abandoning school at the early years of education.

5. Inefficient investments by the Central Government: the politicians have been unable to help the South of Italy economy in any way other than:

• colossal & useless infrastructures: like colossal bridges, dams, highways, aqueducts, etc. in most of the cases never going to be completed (or even pass the initial construction stages). The bridge connecting Sicily to Calabria cost hundreds of millions of Euros already and never passed the “preliminary study” phase.
• subsidy of mega-factories from private companies (most of them would relocate elsewhere once the subsidy ended: e.g. FIAT Auto);
• Periodically hiring a ridiculously high amount of people in the Public Administration before any election cycle (e.g. the Municipality of Naples has now accumulated approximately 20k employees, Rome 23k). These public sector employees are heavily unionised and are able to blackmail any government (local or central alike) willing to update the rules governing their employment, de facto preventing any possible reform of the system which is still the same of 40–50 years ago (having been granted fantastic privileges in the past and having obtained that normal rules pertaining to the private sectors shall not apply to them). In Rome there was a three-day strike by basically all the Municipality employees once the Major of the town proposed to remove their (admittedly) fake “productivity bonus” — a robust salary subsidy given to all Municipality employees without any productivity requirement even being checked. A few months later the Major of Rome had to resign without this reform being passed. Many of these employees are not even required to show up for work: a job in a Municipality is regarded nothing more, nothing less than a sort of welfare subsidy for the employees’ family, without any requirement to carry out any actual job whatsoever.
• The politicians managed to damage the economy even more by regularly awarding public procurement contracts to companies connected with the organised crimes.

6. High level of corruption among Public Officials and State Employees: this is very unfortunate and, until very recently, purposely only blandly punished by the law. The phenomenon is widespread across all sectors and levels of the bureaucracy, political parties, State-owned entities, and it greatly contributed to the draining of resources from the legitimate economy. The former President of Region of Sicily (the highest seat in one of the most populous Italian regions) just finished serving a 7-year jail sentence for being a Mafia-aide. Mr Marcello Dell’Utri, who for a lifetime has been the right-arm of Mr. Berlusconi, is currently in jail in Rome for a similar sentence.

7. Huge «underground» economy: to exacerbate the problem, hundreds of thousands of people are employed in the economic system completely un-registered. These people are often-times paid very low-salaries, have no social-security, do not pay taxes, etc.

8. Ineffective Rule of law: in the southern part of Italy the Government has traditionally weaker control of the territory. For decades, this allowed all sorts of behaviour by people willing to breach the Law with impunity, for example:

• tens of thousands of houses built in environmentally and/or archaeologically protected areas — particularly in Campania, Sicily and Calabria where the local governments have been unable to tear them down after 40 years;
• one of the lowest tax compliance in Europe (the Region of Sicily recently admitted that less than 12% of its tax payment injunctions are eventually paid by its residents: making it a de facto tax heaven in breach of all EU rules).
• longest time for civil proceedings to recover debts;
• millions of civil and criminal proceedings for petty / administrative claims clogging the local Courts.