The Count of Monte Cristo, despite all of its unbelievable (unbelievable in the best possible way, the "oh man, no way did he just do that" way) action and adventure, draws heavily on fact – at least as far as the setting and details go. All the stuff about Napoleon – which you can read more about in the "Why Should I Care?" section – the descriptions of Marseille, the Roman carnival, Parisian society, and the like are true to life; Dumas takes special pleasure in mentioning real opera singers, and his characters can be seen reading real newspapers throughout the book. His geographical descriptions are equally faithful, and you can, if you so choose, trace the itineraries of his various trips through the Mediterranean.
It should come as no surprise, then, that there really is an island of Montecristo located a short distance south of Elba. Dumas's description of the place isn't exact – at one point there was a monastery there, and it may or may not be inhabited by a bunch of wild goats – but it's there, nonetheless, in all its insignificant glory. The name Monte Cristo literally means Mountain of Christ, and, as you might expect, there's a reason Dumas chose a place with such a loaded name instead of, say, the nearby isle of Pianosa; resurrection, redemption, and salvation are a big part of the book, and the "Christ" reference recalls all of these themes.
But we're going to look beyond that for now (you can read more about it in the "Symbols and Imagery" section) because, well, the book is called The COUNT of Monte Cristo and in Dumas's fictional world, there's a lot of meaning invested in such a title. Back in the early nineteenth century just about any old rich dude (nabob, meaning "a man of great or conspicuous wealth" is a good word for those types) could get himself a title. Monte Cristo tells Albert de Morcerf that he's "an accidental count, fabricated by Tuscany with the help of a commandership of Saint Stephen: I should never have passed myself off as a great nobleman were it not that I was repeatedly told this was absolutely necessary for anyone who travels a lot" (41.15). Dumas wants us to know how easy it is to transform oneself in society's eyes. The early nineteenth century was an incredibly tumultuous time for the French and, as we see with Fernand/Morcerf and Danglars, fortunes were made quickly and lost even quicker; names could be bought, could be changed and assumed, and title could no longer be trusted to really signify nobility. The "Count" in the book's name, aside from sounding really cool, is ultimately a nod to that strange and volatile class system that emerged in the years after Napoleon's defeat.