My books are at my house, so I don't really want to go into great specifics yet, but I'll address the surface of it.

For nearly 800 years the Spanish fought to push Moslems who had invaded in the early 700s back out of Iberia. It was a very slow process, as by the late 700s the Moslems had almost complete control of the Iberian Peninsula. Because of these 800 years of almost constant (and at the very least threat thereof) warfare between the Islamic states of the southern Iberian and northern Christian states, employment for knights was not lacking on either side of the conflict. In a few prominent examples, such as that of El Cid, some warriors were even able to switch sides. Also, the Christian kingdoms of northern Iberia were not free of strife amongst themselves, further raising the need for warriors.

The constant need for knights and other military figures left medical Spain flooded with minor nobility. Castile is called such due to the numerous castles built in the area during the period, evidence not only of the need for fortification but also of the uncharacteristically top-heavy feudal system. So many were built that, with contemporary mining technology, the stone reserves of the area were completely exhausted. Since I'm rambling a bit, I'll pull it back in.

During the entire Reconquista there was a strong culture of masculine, military tradition. Due to the ongoing conflicts with the Moors, not to mention the large amounts of strife between the various Spanish kingdoms, a large number of these members of minor nobility found easy employment in Iberian militaries. Even people of relatively low birth could find, in some way a position relating to the war efforts.

Politically speaking, as you noted in the question, in a feudal system like medieval Iberia, success was based on efforts made in the Reconquista. Economically speaking, the top-heavy military society was only kept afloat by the constant warfare.

After the Reconquista, and the subsequent consolidation of northern Iberia, there simply was no further need for soldiers. The great struggle against the Moors complete, the heavily military society struggled to adjust to its success. The religious tone and goal of "Christianizing" Iberia from the Moors (and eventually Jews) was a very important goal of the Reconquista; many Christian leaders considered this as somewhat of an 800 year crusade. This is important because it directly led to the ways in which the Spanish treated their New World populations; but I'll get back to that.

Now, the Iberians had a large military tradition and capacity with no one to fight. The large numbers of nobles were left with no way to prove themselves in battle and thus gain political relevance. There was an entire peninsula of men who wished to prove their masculinity but could not. Unable to support such a top-heavy military apparatus without conflict, many noble families collapsed. The failure of many of these nobles to adapt to the changing times was sarcastically noted in Don Quixote in 1605, though this is slightly later reflection.

Que the Age of Discovery. With a tradition of conquest, crusade, and the honor derived thereof, the men of (and in some cases women!) minor nobility and lower classes of Spain jumped at the opportunity to travel to an unexplored region for a plethora of reasons. On a personal level Conquistadors were motivated by the desire for honor, profit, and relevance. From its roots in the Reconquista, the Christian tradition of the Spanish military enabled the Castilians to justify their exploitation of local populations. As a trade for the knowledge of Christ and eternal salvation, the Spanish were entitled to their riches, land, and labor. As a result, the tradition of conquest really played well into the massive, rapid expansion of Spanish interests in the growing European Age of Discovery.

I'm guessing this is how your book ties into it, I hope it helps. When I go home some time this week, I can look into the books I have on the topic for specifics.