I'll have to fundamentally disagree with the other comment posted.

It's a common misconception that the south was poorer than the north, more crime ridden or less industrially advanced. Sorry to be harsh but that is essentially wrong.

Although industry was not as prevalent as agriculture in the Regno delle Due Sicilie, it was still quite advanced pre-1861. The Regno delle Due Sicilie was actually a leader in a number of industries and was especially advanced when it came to precision industry. If anything, industry provided a larger portion of income in the Regno delle Due Sicilie than it did in any other Italian state. As an example, a 2010 study by the Banca d'Italia (here) seems to give strength to some arguments that had been made for the best part of the 1900s that the economic divide between northern and southern Italy wasn't ever really there before the 1880s. Another study (here) goes as far as suggesting that the average per capita income between north and south in 1860 was virtually identical. Some earlier historians and economists presented data which suggested that public debt was a quarter of the public debt of the Regno di Sardegna, with a more stable inflation rate and the tax system was a lot less onerous.

Another point to make is around the oft repeated point that the north was always much more industrialised than the south, which was essentially agrarian. That fails to recognise the fact that the north was also heavily reliant on agriculture and its industrial character is often exaggerated. Yes, industry was developed but it was nowhere near what it was in other European countries. Outside of the major industrial area of Italy, the Triangolo Industriale (the area between Milan, Turin and Genova), the population in the north was still essentially agrarian. Even within the Triangolo Industriale there were significant areas which saw limited industrial development and were still largely agrarian. As an example, a huge chunk of the land between Milan and Turin was the main rice production area in Italy and still today remains one of the largest rice producing areas in Europe.

The whole point about "localised government in the South" is also essentially wrong. From a polity point of view, the south was much less fractured than the north was until 1861. Although for most of its history the Regno di Napoli and the Regno di Sicilia were de iure separate entities, both had been ruled by the same king since 1130. Contrast that with the north which at the end of the Napoleonic period was subdivided in at least 7 different polities. Unless obviously the statement refers to post-unification Italy, in which case there wasn't any "localised government in the South" and if anything the centralised grip of the court and parliament was exercised quite ruthlessly (see brigantismo).

As for the part about crime and the Mafia, it sounds like straight up pseudo-history with no real basis as an explanation for the economic divide between north and south.

To answer your question OP, no one has come up with an overall answer as to why there is an economic gap between the north and the south of Italy. Most historians will agree that this gap really came to be post-1861 (with many pinpointing the 1880s as the starting point) but there is quite a lot of argument as to the why. Some historians argue that the origin of the gap is to be found in pre-unification conditions and some historians argue that the origins are post-unification and potentially driven by predatory economic policies by a succession of north-centric post-unification governments. It certainly can be argued that at least in the 20th century, a general attitude of indifference by successive Italian governments has done little to reduce the impact of the wealth gap or do anything substantive to close that gap.