caravels, which made exploration possible.

Additionally, the Crusades helped Europeans discover new foods and spices in the Middle East and Asia. What’s so important about spices? Before there was refrigeration, food would spoil easily, making it taste bad. Europeans could use exotic spices like nutmeg, cinnamon, and pepper to flavor their food. Finding spices is what made exploration desirable.

This hunt for spice is what motivated Christopher Columbus to set sail. He was looking for a faster route to India and China so that Spain could trade for spices without having to go through the Arabs and Italians, who controlled the spice trade.

Besides, travelling between Europe and Asia by land was difficult-- there were few roads and there was a lot of warfare. Boat travel was faster, but travelling down around the southern tip of Africa was dangerous (ocean currents frequently blew ships off course). Columbus correctly assumed the Earth was round, but incorrectly assumed that there were no other continents besides Europe, Africa, and Asia. He hoped to sail West from Europe and eventually hit Asia. His theory was correct, but there were two huge continents in the way. (Fun fact-- in each of his three journeys, Columbus never actually made it to the mainland of North or South America. He only explored a few Caribbean islands).

The 15th century was also a time of intellectual curiosity and religious fervor (strong feelings) in Europe. The Renaissance started during this time period, and brought with it a new desire to learn. Many Europeans explored simply because they were curious about the world around them. Furthermore, the fighting against Muslims in the Crusades made many Christian Europeans eager to spread Christianity. Many Europeans explored new lands looking for converts to the Christian faith.

For more information about the Age of Exploration, check out these great eNotes Homework Help answers here and here. 

There were a number of technological and economic factors that contributed to the ability and the desire to explore across the Atlantic.

The monetary system of Europe was still based entirely on gold and silver, so despite expanding trade and economic growth, they had no means of expanding the money supply accordingly without acquiring new sources of gold and silver. Had they been willing to simply adopt a fiat money system, this would not have been necessary; but economic theory was not yet nearly well-developed enough for people to understand that. Actually, there were important changes in the banking system---including double-entry accounting---that allowed the money supply to de facto expand despite the constraints of gold and silver; but they weren't enough, and European governments were constantly searching (or fighting) for new sources of precious metals in order to avoid deflation and economic crises.

While initially Europeans did not know about the New World, they did know that the Earth was round (the Greeks had figured that out centuries ago), and many voyages were initially intended as alternate trade routes to reach India and China. This was indeed Christopher Columbus's stated goal, though part of why it was so hard for him to get funding was that he used a nonstandard (and indeed, wrong) estimate for the size of the Earth in order to make his journey seem easier.

Once they found the New World, European explorers also realized that there were many other valuable new goods to be found there, such as cocoa, corn, tomatoes and potatoes. Once this was discovered, the economic incentive for further exploration became that much greater.

But perhaps the most important change during the Renaissance that led to the Age of Exploration was the improvement in navigation technology. More reliable compasses, better mapmaking techniques, and above all better tools for astronomical navigation such as quadrants and astrolabes made it possible for ships to sail much further than before without getting lost. Another important advancement was the invention of caravels, small, highly maneuverable ships with a new high-tech (for the time) sail that allowed them to sail into the wind much more effectively. Previously there had been reasons to explore the world---but now, at last, there was the technology to do it.