Why were the europeans able to embark on the voyages of exploration in the 15th century?

Europeans were encouraged for overseas voyages in the 15th Century because they wanted to explore America and regions in Africa and Asia. Since they knew little of geography, they took expeditions to satisfy their curiosity especially about the Asia. They are interested in Asian spices, because there are spices that can make food taste better even if it is not fresh. Spices can also preserve food during winter.
However, it was not only about the spices. Europeans also wanted to control the trade routes. That time, it's the Muslims and Italians who were in controlled of the trade routes. Europeans thought that if they found a sea route to Asia, they can gain more power from the trade routes.  Aside from more power, they wanted to spread Christianity.

Another reason is they wanted new opportunities for knowledge and wealth. Explorers back then believed that they will earn wealth, fame and glory if they went on voyage.