There were several factors that led to European exploration and discover new world, to name some are the following:
1. Gospel - Europeans felt compelled to spread the Gospel of Christianity to the world.
2. Technology - Around 1300's advances in ship-building technology led to ships that were sea-worthy enough to travel safely in Ocean. Advances in navigation equipment helped also.
3. Spice - European nations were exposed to numerous types of herbs and spices from the East during the crusades. Europeans pursued to find direct trade route with the suppliers of the spice. Since Muslim countries controlled the land route, Europeans sought new route via sea routes and they were not in friendly terms with the Muslims.