Blazon: Per saltire or and argent; in chief a larch pine eradicated vert, in dexter a cross paté pommettée of eight, in sinister a cross potent sable, in base a Doric capital azure
I’m sure you’ll be shocked to hear that every one of these charges has a specific symbolic and/or historical meaning. The pine tree is both a common species in the region (Pinus nigra laricio, if you’re curious) and a symbol of the region’s natural beauty. The capital is, unsurprisingly, a reference to the area’s legacy as part of Magna Graecia. The dexter cross is representative of the time the region spent as part of the Byzantine Empire, and the sinister cross represents Bohemond I of Antioch and those who accompanied him on the First Crusade. (Bohemond was the son of the count of Apulia and Calabria before he headed off to the Holy Land and founded his own principality.)
The dexter cross seems to be described variously as a Greek cross (no), pommé (sort of?), and a Byzantine cross (maybe, if there was any kind of consensus as to what that means). I don’t think any of those accurately describe what’s depicted here, so I did my best to describe it with the terms I’m familiar with. (In case you can’t tell, I borrowed some of the language from the traditional description of a cross of Toulouse.) The sinister cross is almost definitely supposed to be a cross potent, due to the reference to Jerusalem, but it seems to be drawn more like a very weird cross crosslet.