The borough Queens was discovered by Adrien Block, a Dutch man sailing for the Dutch East India Company, in 1614.  They colonists settled in Manhattan, where they began to build up their community with help from the Natives of the area.  The name Jamaica actually comes from a mistranslation between the Dutch and Native Americans, and has no relation to the country Jamaica.  The Natives dubbed the area “Yameco”, which was native for “beaver”.  However, due to the Dutch pronunciation of the letter “y” as “j”, they wrote the name of the area as “Jamaico”.  After more and more diverse peoples flooded into the area, the name was said as it was written.  Eventually, the “o” at the end was turned into an “a” because it was simpler to pronounce the “a” than a hard “o”.

In July of 1968, Congress reconstructed the strict statutes surrounding immigration, allowing people from less-developed countries to finally come to America.  This caused an enormous influx of ethnicities from other countries to come into New York and settle there.  Queens is now considered to be the most diverse county in the country because of this surge.  There is no clear reason as to why Africans and other blacks settled in Jamaica, other than most obviously that that is where they were led and decided to stay there.

http://www.thirteen.org/queens/history.html