Slavery in the Americas is rather a big topic to discuss in such a short space. I guess you could say that its nature was that it was racial slavery with only blacks being enslaved (for the most part). Also, the slaves were mainly used for agricultural work.
The slaves were connected to the economy of the Americas because they provided much of the value that made the Americas rich. This was especially true in the Caribbean. The slaves were connected to the African economy because the slave traders brought many goods and other resources into that economy to use to buy the slaves. Of course, taking the slaves away hurt the African economy by depriving it of human resources.
It was very closely linked to the economies of these places in that the slave trade lasted for centuries, and in both a barter system and a monetary system of trade, stimulated the demand and movement of goods to and from the New World to Europe, Africa, North and South America and the Caribbean.
The triangular trade involved the shipment of molasses, rum and slaves in a perpetual three way economy that moved tens of thousands of human beings, and millions in commercial goods. This helped to develop the new world colonies as they increasingly used slavery to plant and harvest cash crops such as sugar and tobacco.
In Africa, as the slave trade grew, local tribes would kidnap members of neighboring and enemy tribes to sell or trade to the Spanish and British, bringing material and finished goods to the shores of Africa for the first time.