Final answer:
Portugal and Spain were motivated by the pursuit of wealth from the lucrative spice trade and the religious goal of spreading Christianity and counteracting Islam. These twin desires led to significant exploration and eventual conquest across the Atlantic.
Step-by-step explanation:
The religious and economic motives for Portugal and Spain's exploration and the associated risks during the Age of Discovery were driven by a combination of factors. The lure of the lucrative spice trade with Asia, which would not only enrich these nations but also weaken the Muslim world, was a major economic incentive. Spices such as cloves, pepper, and ginger were highly sought after in Europe, and the Portuguese and Spanish sought new trade routes to bypass the Muslim traders who dominated the trade from Asia.
From a religious perspective, the desire to spread Christianity and counter the influence of Islam was also powerful. This urge was partly rooted in legend, such as stories of Prester John, a mythical Christian king. The Portuguese, in particular, hoped to ally with Prester John to fight against Muslim forces and saw exploration as a means to that end. Moreover, the Spanish conquests were partly fueled by a mission to both spread Christianity and bring glory to their empire.
Ultimately, the combination of seeking wealth through direct access to spices and other trade commodities, and the pursuit of religious objectives, namely the expansion of Christianity, motivated the Iberian kingdoms to undertake the perilous journeys across the unknown waters of the Atlantic.