What advantages did European nations have over others in regards to colonization?

First, European nations developed or acquired, earlier than other peoples around the world, many of the technologies necessary for colonization. These included nautical innovations like the caravel (a vessel suited for long voyages,) the compass and the astrolabe (important tools for navigation) and special sails that made exploration possible. But Europeans also developed weapons, including steel and firearms, that facilitated the conquest of people around the world.
Another advantage was in many ways highly ironic. Europeans, having had many domesticated animals for thousands of years, had developed diseases, including smallpox, typhus, measles, and plague, most of which originated with these animals. Native peoples in places like the Americas and Australia had no such animals, and thus no exposure to such diseases. So when Europeans came in contact with these people, the germs they carried led to what are sometimes called "virgin-soil" epidemics that wiped out millions of indigenous peoples. The combination of disease and superior weapons enabled Europeans to conquer and colonize peoples in the Americas in particular. The Inca, for example, were among the most powerful empires in South America, but Spanish conquistadores, especially Pizarro, were able to conquer them because the Inca so depleted by a smallpox epidemic. Thus these diseases, whch had periodically ravaged Europe, proved to be potent "weapons," even if Europeans did not intentionally introduce them. One writer, Jared Diamond, has characterized these mutually reinforcing advantages as "guns, germs, and steel" in a book by that title. 
Once Europeans came in contact with Indian peoples, they were able to spread information about them through print. Where Native peoples were often taken by surprise, at least at first, by contact with Europeans, colonizers were armed with knowledge about other Indian peoples. This could prove, however, to be detrimental, as England's Jamestown colonists thought they could replicate the Spanish model of conquest and colonization among the Powhatan peoples. They were mistaken, and the approach they took was almost their undoing. But Europeans could share information about the peoples they colonized, a fact that facilitated their conquest. 
Finally, all of these things also enabled Europeans to eventually dominate Indian trade, even if they could not conquer Native peoples. Europeans were able to trade for slaves, foodstuffs, and desirable items like deerskins, a process that led to the subjugation of many Indian peoples. The economic changes led to even more social turmoil among Indians, a condition that eventually led to their subjugation in many cases.