3 factors drove Europeans to start sea exploration. God, gold and glory.
Most Europeans at this time saw the opportunity to get rich and make a name for themselves like Columbus. There was a great desire to find a new route from Europe to Asia so Europeans wouldn't have to travel across the Silk Road which was hostile to them.
Thus Europeans started to try and figure out how they could travel to Asia--whether it was by sailing West or around the Cape of Good Hope in Africa.