Why did Columbus want to go to China? Pretty much the same reason that Westerner's go  to China in our own age. Trade goods and turn a profit. Also a sense of adventure in visiting a exotic land. A image which was made popular by the writings of Marco Polo. Some of the goods that Europe craved for in the Fifteenth  Century  were spices and silk. When the Muslims conquered Constantinople (present day Istanbul) the overland trade to Asia became more difficult.This spark a quest to find a sea route to the far east.

 

Of course Christopher Columbus went to his death bed thinking that he had made it  to Asia by sailing west from  Europe .Columbus wasn't the first European to set foot on American. Vikings from Norway sailed  to Iceland and Greenland. Finally reaching North America  in present day Labrador on the northeast Canadian coast. About 500 years before Columbus landed in the West Indies. While Europe remained ignorant of the Viking expeditions to the New World. Columbus' voyages  were to be well known and others soon followed. Still thinking Columbus had reach Asia it took  a few years before it was realized this was a new continent.The credit for this discovery and naming this new land mass goes to Amerigo Vespucci. The name America is derived from his first name.

 So Columbus trying to sail west to China. Accidentally started a new wave to search and settled North and South America.