Christopher Columbus went on his voyages for two reasons, in my opinion -- money and glory.
In the time of Columbus, the spice trade with places like India and Indonesia was extremely important and very lucrative. Columbus believed that he could find a way to get to Indonesia by sailing west. If he could do that, whoever sponsored him would be able to get in on the spice trade that was, at this time, mainly in the hands of the Italians (via the Middle East) and the Portuguese (by sailing around Africa).
Columbus also wanted the glory of being the first to sail that route. He wanted to be known as a person who figured out a way to Indonesia that no one else had discovered.
All in all, then, Columbus wanted to get rich and he wanted the glory of finding a new sailing route to "the Indies."