Europeans really did not explore in any important way in the 14th century. In that century, the technology needed for exploring was not present. In addition, European countries had other issues. France and England spent much of the century fighting in the Hundred Years War. Spain still had Muslims to fight on the Iberian Peninsula. The Black Death decimated the population in the middle of the century.
It was not until the 1400s that much European exploration started. This began with Portuguese expeditions down the coast of Africa. At that point, the motives were mainly:
- Curiosity. There was interest in finding out if all sorts of wild tales that were told at the time were true. For example, there was a desire to find the kingdom of "Prester John" and other supposedly lost Christian civilizations in Africa and India.
- Trade. The Portuguese wanted to find a way to trade directly with Asia. They wanted to bypass Muslim middlemen and go get spices directly from the source.
- Religion. There was some desire to spread Christianity to new lands.