There were many economic factors such as competition. The Ottoman Empire had risen to prominence leading up to period of European colonization. They controlled many of the trade routes to the east, and Europeans would have had to pay to use them. So, while it was obviously an economic risk to send ships out into the unknown, the conditions of the time made it a worthwhile gamble and there was a snowball effect once resources started coming back from the New World. In the absence of an empire in Western Europe, there was great competition between powers which sped up the race to colonize. China was already powerful during this period (Ming dynasty). You had the Mughal Empire in northern India, Ottoman Empire, etc. I am not trying to say that these established powers did not try to expand using new strategies, but just think about what risks an internet start-up can take today compared to an established company like IBM or Microsoft, and the kind of disruptive economic growth happens as a result.

In addition to the economic factors, you must consider the geographic advantage that European countries had at the time. They were better positioned to send out expeditions than any of the powers in the east. It was not as feasible for, say China or Japan to send ships over the Pacific Ocean because of the long journey. They could and did take ships other places, but these places often had established powers and were not nearly as easy to conquer as the Americas proved to be. Meanwhile, after Gibraltar fell from Islamic control towards the end of the 1400s, European ships were able to get safe passage out of the Mediterranean Sea and then further west.

This brings me to the most important factor in this period of colonization, and the reason why the Americas were a desirable place to colonize: The vast majority of Native Americans were killed by germs that the Europeans brought over. This effect streamlined the process of domination in a way that the Eastern powers could only dream of. The Mongol Empire certainly dominated Asia in dramatic fashion years before this period of European colonization, but they failed to conquer Japan in two separate campaigns. Just think of what they could have accomplished with the aid of these killer germs!