Perhaps their most significant accomplishment (because it helped lead to various others) was their promotion of greater unity in Spain. By marrying and uniting their two kingdoms, they helped to promote the growth of Spain as a nation-state in the modern sense of the word.
Queen Isabella and King Ferdinand wanted to rid Spain of heretics (defined by them as anyone who was not a Catholic) By the time they came to the throne in 1474, Spain's population included a significant number of Jews, Jews who officially converted to Christianity but kept Jewish tradition, and Muslims. Over the next few years Isabella was influenced by the ideology of Tomas de Torquemada, who believed that those who were non-christian or did not truly believe in Christianity be persecuted. This crusading and nationalistic mindset led Isabella and Ferdinand to ask Pope Sixtus IV for permission to begin an inquistion. Referred to as the Spanish Inquistion, it consolidated Isabella and Ferdinand's power, promoted their 'true' religion, punished and tortured those who hid behind 'false conversions'. In addition, the Pope designated Isabella's mentor Torquemada as the general of the inquistion in Spain. In doing this the Pope essentially deferred absolute control of the Spanish Inquistion to Isabella and Ferdinand.
Some of the other important actions of their reign had to do with the marriages and other alliances they arranged that would later lead to the successful unification of Spain for their successor and they also laid the groundwork for the most powerful and successful military of the next few decades after their rule.
The two most important events during their reign were the Reconquista and the "discovery" of the Americas. It was under Ferdinand and Isabella that the Muslims were driven out of Iberia once and for all. This helped free them to support Columbus on his attempts to reach the Indies by sailing west.