What European conditions led to the conquest of the Americas?

Portugal began to explore sea routes to the far east in the first decades of the 15th century, and Spain was not far behind them.  Interestingly, King Ferdinand and Queen Isabella of Spain regarded the exploration between the two monarchies as something of a contest. So much so, that they ultimately signed a treaty between them and Portugal to divide the New World evenly among them. In addition, it was not long after the exploration by Portugal and Spain that France and England joined in the discovery of the New World. However, there was a common denominator among these monarchies that led to their 'success' in their exploration and conquest of the New World, better technology.  Between 1350-1450 each of  these countries developed their map skills, navigational capacities (due to the northern point compass), and advancements in ship building. There is no doubt that these conditional components allowed Europe to engage in the New World.

The major condition in Europe that led to the original conquest of the Americas was peace.  This applies mainly to Spain which, of course, was the country that was first involved in conquering the New World.

Spain came to be able to explore because of the coming of peace.  Up until 1492, the Spanish had been involved in wars against the Muslims, trying to push them out of the Iberian Peninsula.  But then the Spanish won that struggle and were at peace.  At that point, they were able to put their money towards exploration.  Once Columbus "discovered" the New World, the Spanish were able to send soldiers to conquer who were no longer needed for wars in Spain itself.

What European conditions led to the discovery and conquest of America?

There were any number of things which led Europe to expand beyond its borders; the discovery and conquest of America was incidental to that expansion, which also extended into Asia:

• There was also renewed interest in the art of navigation: The principle of the Compass was known in the twelfth century; but by the 15th century, the astrolabe allowed one to navigate at night for long distances outside the sight of land.
• The rise of towns had given rise to a growth in trade with profit the driving motive.. Trade with the far East had originated as early as the Crusades when crusading knights at Constantinople and other areas saw products of orient; silk, spices, dyes, perfumes, rugs, even oranges. Trade continued throughout the Mediterranean world with Arab and Christian merchants frequently trading with one another.
• The Description of the World; or The Travels of Marco Polo (1298-1299), provided impetus for trade and exploration. Although there is some speculation about the accuracy of his book and even its authorship; it was widely read and increased speculation about travel to the East. Christopher Columbus kept a copy of Marco Polo's book which was annotated in Latin.
• The rise of nation states. Ruling monarchs had the power and money to sponsor a search for a water route to Asia. This worked well also for merchants, who wanted a uniform currency, trade laws, and the elimination of trade barriers. Important incidences were the marriage of Ferdinand and Isabella to form modern Spain; and the defeat of Richard III at the Battle of Bosworth Field by Henry VII.
• The Crusades were also important. European crusaders had had contact with Eastern Monarchs –there was no feudal system in the Orient. They also learned of new weapons, gunpowder, and developed standing armies; all of this made Monarchs stronger and feudal lords weaker.