Geography:
Everyone knows that, because of the Ottoman stranglehold on the spice trade, the Spanish and Portuguese sought out their own trade routes in order to bypass interaction with the Ottomans. This eventually led to the Portuguese sailing around Africa, and the Spanish finding the new world and sailing around southern America to reach eastern Asia.
Now, if you look at a map of Europe, the nations of Iberia where perfectly positioned to explore and colonize the world. Portugal, for one, only had to worry about keeping friendly relations with Spain, as no other nation had a direct land border with them and thus, would have an extraordinarily hard time invading the nation. The Spaniards had enemies in north Africa, and also in southern Iberia (until they conquered Granada), but this did not last long at all, as the Spaniards where seperated from north africa via the strait of Gibraltar. Not to mention the fact that Iberia is the west-most point of Europe (unless you count Iceland and Ireland).
Technological Advancements:
The Europeans had many technological advancements that they adopted from many other nations. Gunpowder, the Sextant, and the Caravel where all instrumental in European Exploration and colonization. By the 19th century, Western Europe was exponentially more advanced than the rest of the world, partially in thanks to the industrial revolution. It was during this century that South and SE asia as well as Africa where conquered and split by many multiple European nations.
Lack Of Foreign Competition:
In the early age of exploration, there where only a few nations that could have begun exploring and colonization either before or alongside the Europeans, however, none of these nations did so. China decided to send treasure fleets Westward instead of Eastward across the pacific, where they would have found the new world, and the account of the Mali Empire discovering South America are dubious at best, although it could have been possible.
Disease:
The European explorers brought many diseases with them on their journeys, including smallpox. These such diseases spread through New World Native populations, wiping some of them out entirely and leaving the vast agricultural and mineral resources for the Spanish to exploit with little to no resistance. There was heavy resistance at first, especially during the 16th and 15th centuries, where the Spaniards had to compete with other South American empires such as the Incans and highly militaristic Mayans. After these initial conquests were completed, resistance to Spanish occupation was almost entirely restricted to rebellions and uprisings, as opposed to wars. Not to mention the fact that the Spanish empire had quickly grown into not only the first Atlantic empire, but also the first major colonial power.
