The growth of exploration and the development of new revenue streams in the colonies played a very large role in the development of slavery. The land in many of the colonies was agricultural based, with many cash crops such as tobacco and cotton. The harvesting and development of these land areas became of critical importance. With the emergence of the finances these areas offered, a bartering system based off of money and goods allowed slavery to grow. One such system was called Triangular trade, where a triangle emerged between the three points of the the African coast, where slaves were taken for money, to the West Indies, a mid point where bartering for slaves in exchange for money and other goods developed to the New World, where slaves were purchased and bought. The growth of Triangular Trade helped to make slavery a permanent part of the New World.
Slavery had been around a long time before it came to the New World. Europeans knew about it from Biblical times and from the Greeks and Romans. So when it started in the New World, it was really just a continuation of what had been going on in the Old World.
The Europeans started getting African slaves from Arab slave traders as soon as they started exploring Africa. They really didn't need many slaves at first, but they found out about that source of slaves.
Later, European countries started to colonize the New World. They found out that they needed slave labor. So they went back to the main source of slaves that they knew about -- Africa.
I edited your question, and am assuming that you were referring to so-called "modern slavery" from the 1500's on in the Western Hemisphere.
This system came out of the need for empires to have a large and permanent labor force to cultivate cash crops such as sugar and tobacco in South America, the Caribbean and North America. Empires such as the Portuguese and Spanish were among the first to kidnap and use large numbers of West African slaves. Over 3 million were taken to Brazil alone, and over 250,000 to the present day United States.
Please re-edit your question if this does not address the aspect of slavery you need.