What developments in Spain had just taken place as Columbus set sail?
One significant event that occurred right before Columbus set sail into the Atlantic was the completion of the Reconquista. This was a series of long and bloody wars between Christian kingdoms and Muslim peoples originally from North Africa who had established a presence on the Iberian peninsula 700 years earlier. In 1492, the Christian kingdoms of Castile and Aragon won a final victory over Muslim forces in Granada, permanently uniting the Iberian peninsula under their control. This was a major step on the path to creating Spain as a kingdom-state, albeit one that was very diverse ethnically. The other important event, one which actually made the final Reconquista possible, was the marriage of Ferdinand of Aragon to Isabella of Castile in 1479. Castile and Aragon were the two most powerful Christian kingdoms on the Iberian peninsula (except perhaps Portugal) and their marriage united these kingdoms.
These two developments contributed to Spanish exploration and empire-building overseas in several important ways. First, they created Spain as a powerful kingdom with the finances and the ambition to support overseas exploration. Second, the Reconquista in particular gave rise to a warrior class of inferior nobles who sought opportunities to expand their power and influence through warfare. After the conquest of Spain was complete, they wanted new opportunities for power, riches, and glory. It also aroused in Spain a crusading spirit that they carried to the New World, one which had devastating consequences for Indian peoples there. So Columbus set sail on behalf of a kingdom that was just emerging as a European power, one which was aggressive, ambitious, and newly unified.