Hi, finally a question i can contribute to.
In the 15th century, Spain(as in Castilia-Aragon, but i'll just call it Spain for simplicity reasons) was busy with their Reconquista, while their Rival Portugal was able to start with Naval Exploration much earlier than Spain. Getting past the Southern tip of Africa by 1488 (Bartholomeu Diaz), and winning Hegemony over Spain at Atlantic Exploration with the Treaty of Alcacovas 1479, which granted Portugal all discoveries in the Atlantic, in exchange for the Canary Islands. By the Conquest of Granada in 1492, Spain had a lot of ground to cover. That moved the Catholic Kings to funding Columbus' Expedition.
Before this, Columbus tried to get his expedition funded in Portugal, however he was unsuccessful because of severe Inconsistencies in his math. Columbus calculated around 2500 Nautical Miles from Portugal to Japan, instead of over 10000. He miscalculated the circumference of the globe as well as the width of a degree of longitude. The counselors at the portuguese court recognized these errors and declined him.
But since Spain had the financial capacity after Granada, and was desperate enough to take the chance with Columbus (who my Professor for medieval History called a "überbewerteter Glücksritter") to maybe gain back the aforementioned ground they had lost to portugal.
Now after Columbus' expedition was successful, Spain got into more Problems with Portugal which resulted in the Treaty of Tordesillas, after the papal Bulls (Inter caetera divinam) of Alexander VI. proved unsatisfactory. Said treaty split the world in two spheres of Influence on a Meridian line west of the Capverdes, the eastern one being Portuguese, the western one Spanish. But I guess we can save that one for another episode.
As for literature, I can recommend "Ferdinand und Isabella" by Joseph Perez, which should cover your questions on this subject very well.
Hope this counts as indepth enough, i'm on Holiday and on Mobile so resources were limited. I'm open to further questions in replies if there are any.