What factors led to Europe's increased exploration and to the discovery of the New World?

The Age of Exploration (in most history textbooks, this term is used to refer to a period from the fifteenth century until the late seventeenth or early eighteenth century) was enabled by a number of technological advancements in Europe. Many of these advancements in navigational tools, weapons, and shipbuilding are seen as products of the Renaissance, but it is important to note that, in some cases, the Europeans adapted technologies originally invented elsewhere.
Why did the Europeans take to the seas? Historians agree on a set of key factors:
1. The Ottoman Empire blocked land routes to Asia. In order to keep trading with Asia, the Europeans realized they would have to find a water route. European merchants felt that trade with Asia was a necessity, as losing those trading partnerships would allow Arab merchants to outstrip them. European merchants were interested in a number of luxury goods, but perhaps nothing was more valuable to them than spices. Spices were valued not only for use in food, but also for use in medicine.
2. The Age of Exploration coincided with the rise of what many history textbooks call "New Monarchies," or monarchies that were more centralized and independent of the Roman Catholic Church. Examples include France, Spain, and England. The new monarchs were anxious to gain prestige and build reputations, and patronizing successful, aggressive exploration was a way to accomplish that.
3. In some cases, there was a missionary element to exploration. In other words, the Europeans wanted to convert people to Christianity. Although we tend to associate this behavior with the Catholic Spanish, both Catholic and Protestant Europeans worked to convert non-Europeans.
4. Some historians believe the general spirit of intellectual curiosity that marked the Renaissance motivated some European explorers.
As we know, the New World was discovered by Europeans (though of course it was already known to those who lived there) because Christopher Columbus was attempting to discover a western sea route to Asia. A western route was an attractive alternative to the long and sometimes dangerous routes that were previously available: either around the entire continent of Africa by sea or through the Mediterranean Sea and then over land.
http://faculty.uml.edu/ccarlsmith/teaching/43.105/PDFs/Age%20of%20Exploration.pdf