The reasons for Spain's interest in Columbus's voyages start in the year 1453 with the fall of Constantinople. The capital of the waining Byzantine empire was the trade hub between the indies and the people of Europe back in the 14th century, and when it finally fell to the Ottoman Turks, the merchants and heads of Europe began looking for other options. They weren't thrilled with the idea of trading with an aggressive Muslim nation, nor were they willing to pay the extra amount tacked on to the price of the trade goods.
With this setting in mind, the kings and queens of western Europe began listening to new and radical ideas about navigation and global positioning. Enter Christopher Columbus. The Genovese navigator was traveling the courts of Europe with an unlikely proposal regarding a new route to the Orient that most people thought was crazy. He proposed that the size of the earth was actually much smaller, and that by traveling west, you could arrive in the indies faster than any other known sailing route.
Most people thought he was dead wrong, but the newly-crowned king and queen of Spain were willing to listen. At first they too were skeptical, but when they considered the what such a route when mean for them if he was actually right, they decided to risk funding the venture, and Columbus sailed off to the New World in 1492. It turned out that this gamble paid off, and soon Spain was the richest and most powerful nation in Europe.