I assume that you are asking about the European explorers who began exploring in the 1400s. In other words, I assume that you are not referring to people like the Viking explorers who made it to North America centuries before. If you are talking about these explorers, there are three main goals that encouraged them to explore.
One goal was spreading Christianity. Europeans of the time believed that only Christians could avoid going to Hell after they died. They believed that God wanted them to spread Christianity and save souls. Therefore, it was important to find new lands and spread the Gospel to those lands.
A second goal was gaining glory for themselves and their countries. Explorers wanted to gain the fame that went with finding important new lands or important routes to known lands. The rulers who sent those explorers out to explore wanted the glory of having new lands that they could claim as their own.
A final goal (in my view, the most important), was to get rich. Explorers like Columbus could get rich because they might be granted the right to rule and exploit new lands that they discovered. Explorers could also make money through trading. Monarchs (and explorers) hoped that they would find natural resources like gold and silver. These things could help their countries (and themselves) get richer.
These were the three main goals of the first European explorers.