The push for exploration, driven in part by men like Henry the Navigator, was caused largely by the desire for trade.
By the 1400s, Europeans had a strong taste for spices from Southeast Asia. At that time, no one had yet sailed from Europe and around the southern tip of Africa as a way of reaching Southeast Asia. This meant that spices had to come overland across the Muslim territories and then by sea to Italy. The Spanish and the Portuguese, in particular, wanted to break this Muslim and Italian monopoly. For this reason, they started exploring the coast of Africa. They eventually discovered the way around that continent and later, of course, discovered the Americas while searching for trade routes to Asia.