There were many factors that led to the European Age of Exploration. Three of the major ones had to do with the advent and adoption of new technologies, a desire to improve trade by discovering new routes, and a yearning to spread their religion to new lands.
Before the fifteenth century (with the exception of the Vikings), Europeans simply did not have the technology or seafaring knowledge to make long ocean voyages. However, the Renaissance was a time of new learning and advancements in understanding the sciences.
By studying the Ancient Greeks, Europeans unlocked knowledge that had been unstudied for centuries. For instance, Ptolemy had written a guide to cartography in the second century CE. Italian scholars translated this work and used it to help sailors explore new shores. European mapmaking only got more sophisticated from there. German cartographer Gerardus Mercator added lines of latitude and longitude to his famous map, making it easier for navigators to explore.
Ship design also improved. Crusaders returning from the Middle East brought back designs that the Arabs used for their vessels which greatly improved European ones. This included the triangular sail, which allows ships to sail much closer to the direction of the wind and greatly improved their ability to sail to new lands.
New weapons technology also helped the European explorers. Advances in gunpowder technology and steel made it possible for European explorers to intimidate and subdue the peoples that they encountered.
The primary motive for exploration at the beginning of this period was a desire for better trade routes. For centuries, Europeans had been trading with East Asia by indirect overland routes, such as the famed Silk Road. These routes brought in such luxury items as silk, spices, and fine ceramics. However, due to the many middlemen involved, this method of commerce was very expensive. If a nation could control a direct sea route to the East, then they could better reap a bigger profit. Furthermore, during times of conflict, such as the Crusades, Muslims along these routes would shut off trade with Europeans altogether.
The desire to spread Christianity was also a major motive for European explorers. This period of exploration coincided with the Reformation. This great clash between the Catholic establishment and new Protestant sects led to missionaries following close behind explorers, eagerly spreading their faith to new populations.