The factors that led to European exploration in the 15th century were multi-faceted. Initially, they were motivated by a desire to find faster and cheaper trade routes to Asia, where they could trade for spices. Spices were a lucrative commodity in Europe. For centuries, the spice trade was dominated by Muslim merchants who brought these spices to Europe through overland routes and charged a high premium for them. European merchants hoped that by establishing their own sea-routes, they could go directly to the source and gain better access to the spice trade. This was the primary motivation of Vasco de Gama and Christopher Columbus.
Another factor that aided European exploration during this period was improvements in sea-going technology. Better ship-building techniques and navigational advances, such as an improved compass and sextant, in combination with advances in cartography (map-making) meant that it became easier, faster, and relatively safer for European sailors to head out on long voyages.
There was a competitive aspect as well. For instance, Portugal and Spain were in a competition for access to better trade routes. They each figured that control of certain routes and foreign markets meant that they could get the upper hand over each other both economically and politically. A similar sense of competition existed between various Italian states. This sense of competition compelled many to set out on voyages of exploration.
Also, while it would become more of a motivation during the 16th century, the desire to spread Christianity was yet another reason for exploration. Most of the inhabitants of the lands beyond Europe belonged to other faiths, and there was a strong desire by many Europeans to evangelize in these new lands.
In part, technological advances led to European exploration in the fifteenth century. These advances included the caravel, a fast ship that could sail farther than previous ships, and devices such as the astrolabe and compass that allowed mariners to navigate. Improvements in cartography, or mapmaking, also aided exploration.
European nations were motivated to explore for economic reasons as well. They wanted spices and other trade items from the East and did not want to pay middle men to secure these goods for them. This was, in fact, one of Columbus's main motivations for journeying to the New World, which he thought was the Far East.
Nations were also motivated by a sense of nationalism, or national pride, to best other nations. These beliefs were partly ideological and partly economic. For example, European nations' belief in mercantilism, the idea that the country that had compiled the most gold and silver bullion had bested the other countries, drove nations such as Spain to explore the world.
There were several factors that led to European exploration in the 15th century. One factor was the desire to find a shorter route to Asia. The Europeans were trading with Asia, and the land route to Asia was a difficult and dangerous route to travel. The Europeans hoped they might find quicker routes to Asia, either by going around Africa, as Vasco da Gama did, or by heading west, as Christopher Columbus did.
Another factor was the desire to convert people to Christianity. When new lands were discovered, the Europeans learned that the people living in these lands were not Christian. Thus, the Europeans saw an opportunity to spread their religion to other places.
Finally, the desire for land, wealth, and power were factors encouraging exploration. The European powers were constantly competing with each other for influence. Each country knew that if it controlled more land, the land would help their country become stronger. Once it was known that there were mineral resources in these new lands, the Europeans hoped to use these mineral resources to make their countries stronger from a financial standpoint. These lands could also help increase trade for the European countries.
There were many factors that led to European exploration in the 15th century.
Further Reading
I think that the second post means to use the word "imperial," not "empirical." Those are very different things.
The formula that is often used to describe the Europeans' motives is "God, gold, and glory." The Europeans went out for God (to Christianize the heathens in the rest of the world), for gold (to get rich) and for glory (to become famous for being the first to "find" one thing or another.
It is up to each person individually to decide which of these "g" words actually had the most to do with the Europeans' decision to go exploring.
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