Is there any correlation with the Christian retaking Iberian Peninsula in the 1400s and the European exploration shortly afterword? Were there technologies or maps left over that aided in seafaring?

So there is two sides to this. The first is why they felt they needed to, and the second, why they were so successful. /u/DarthObamious elucidates that the Spanish (at this time still Castilian and Aragonese) funding of Columbus's expedition was almost certainly a bit of a hail mary. It's important to remember that, as Darth mentions, pretty much everyone knew that Columbus's numbers were way way off. It is possible that Isabella and Ferdinand were that gullible, but it seems unlikely.

So what is the situation in Iberia that might force them to make this hail mary? Well, consider the previous history. Castile had just spent the better part of four centuries nearly constantly expanding. This created two big problems. First, war isn't cheap. To pay for expansion, campaigns, and settlement takes a large wallet, and the Castilian and Aragonese crowns were both feeling the pinch. With Portugal trailblazing the route to India (by 1492, it was clear it was only a matter of when, not if, the Portuguese would find there way there), the increasing dominance of Venice and Genoa in Mediterranean trade, and the final running out of spoils to help fund wars, the two crowns were facing a bit of a problem come 1492; yes they had finally finished off the Reconquista, but what now? And with war, particularly religious war, being such an ingrained concept, perhaps a core component of their cultural identity, how do you come to terms with no longer expanding? The result of these challenges wasn't simply the funding of the hail mary of Columbus's expedition. 1492 was also the year that the Jews were expelled from Castile and Aragon. There were quite a few ways this was connected. Jewish lenders were probably the single biggest debt holders to the crown and large estate holders, while the terms of the expulsion also mandated that they couldn't take any of their money with them. In this sense the timing makes pretty good sense, since it kills two birds with one stone: satisfy the religious fervor that has been cultivated over the centuries, and get a bunch of free money (and erase significant debts). Expelling the Jews would have significant negative impacts long term on Spain (and particularly Aragon) but that's another story. I think even Ferdinand understood it was a bit of a case of cutting off your nose to spite your face, but that's how it goes when things are starting to get a bit desperate.

So the second part of this is, why were the Spanish so successful? It wasn't because of maps left by Muslims (indeed, the Spanish were more concerned with getting their hands on Portuguese charts). Once the New World was discovered, it was a very short period (within a year) that the first 'colonists' arrived. Instead, it was the state that the Reconquista created that is really the factor here. For generations, Castile's second and third sons, and even foreigners with an urge for the big score (such as Columbus!) had gone to Iberia to try their luck at winning land and wealth. Very few other places in Western Europe could you find better chances at that (only East Prussia is probably comparable). When those opportunities suddenly run out, you have a lot of men who suddenly find their career ceilings reached. But luckily, you suddenly have a land of riches described by Columbus, and a new period of expansion can begin. Heretics, particularly in the post 1492 period, were not looked upon kindly by the Spanish. As a culture that had been invading and approprating the land and wealth of said heretics for centuries, there was an ingrained fervor there that helped them justify both their expansion and enslavement. And those second and third sons? Or the men of lesser nobility? Well, look no further than Cortes, the conquerer of the Aztecs. A man born to a decent name but few prospects, a century earlier he could have raised himself and his family up through raids and campaigns against the remains of the Muslim states. With the new world now open to them, those same energies could be applied against a new set of heretics.