The best explanation that I have seen is offered by Eric Williams in his work Capitalism and Slavery. It goes basically like this:

In the New World of the 16th century, you have a very limited supply of labor and a vast, practically unlimited supply of free land (ignoring, of course, any native inhabitants on said land). This creates a situation where labor is very, very expensive, because any free laborer can simply pack up shop, move up the river towards the interior and found his very own farm. Why work for someone else when you can work for yourself? Under these circumstances, only unfree labor will really work in the long term.

In the New World there are three sources of unfree labor: the native American population, the European population, and imported African slaves. The Native American population was ill-suited for unfree labor, primarily because they could not be easily controlled. Natives could escape back into the land, and owing to their being natives, will actually be able to survive, knowledge of the local environment - things as simply as knowing which plants you can eat and which you cannot, how to hunt the game of the area, etc. Europeans are slightly better as unfree labor. They certainly cannot escape back into environment, but they can escape to another colony or city, where they could blend in with the local settler population. Despite that, unfree European labor, in the form of indentured servitude, was actually quite common in the New World. The final option is imported African slave labor. It had neither of the advantages available to Europeans or Native Americans. African slaves would know little of the local flora and fauna of the New World, and so were less likely to effectively escape in the first generations, until that knowledge was built up within their communities. By the virtue of their black skin, they could not escape to another city or colony to blend in with the settler population either. The practice of bringing Africans from different parts of Africa, belonging to different ethnic groups and speaking different languages only added to the inherent disadvantages the imported African slave faced. As such, it made the most economic sense to import African slaves to perform the unfree labor necessary to make the plantations viable economic units, or so Williams argument goes, if I recall correctly (it's been a bit).

It should be noted that the racism that accompanies slavery was a result of this economic situation, not the cause of it. Europeans enslaved Africans and only later justified it through notions of the racial superiority of the European or the inherent inferiority of the African, not the other way around.

For geographical reasons, Asia was not an option for importing unfree labor. The Pacific Ocean is some 12,000 miles wide, which is almost half the circumference of the earth. Add the land mass of the Americas (since it was colonized from the East), which ranges from about 2500 miles wide in Peru/Brazil to over 3000 miles wide in the United States, and you can see that it's actually closer to get to China from the eastern coast of the Americas by heading east, across the Atlantic, over Europe and/or Africa, and then through Asia, than it would be to go west, over America and across the Pacific ocean. I say all of this only to drive home the huge distances involved.