The first African slave arrived in Hispaniola, the island that now comprises both the Dominican Republic and Haiti, in 1502, ten years after Columbus accidentally sailed to Dominica in 1492.

The Age of Exploration, of which Columbus was a part, was motivated by Europe's demand for goods that they could not obtain within the continent, such as spices and sugar. Trade with Asian and African kingdoms allowed for European nations to obtain their desired goods. Europeans obtained slaves from West Africa as a result of their trading goods that were coveted by chieftains and kings, such as firearms. Some Africans were forcibly stolen without the cooperation of tribal leaders, as was the case in present-day Angola when, in the early 1600s, Queen Nzinga resisted abuses by Portuguese traders. She did this partly with the help of the Dutch, with whom she had formed an alliance.

As previous educators mentioned, the demand for colonial goods, such as sugar, tobacco, and, later, cotton, required a constant and cheap source of labor so that colonialists could both pay the steep taxes imposed by colonial powers and make profits. In North America, indentured servants, most of them from England and some from Ireland, were sent to work in the colonies. In exchange for some years of labor, they would receive a parcel of land. However, this proved to be a bad business model. White indentured servants balked at long hours of back-breaking labor. Furthermore, the requirement of land in exchange for labor threatened planters economically by creating more competition in the marketplace.

Indigenous people were enslaved initially, but, as a previous educator mentioned, some fled. Many others proved to be very vulnerable to European viruses, such as influenza and smallpox, and the natives died in vast numbers. Colonialists required a labor force that could withstand the tropical and near-tropical climates in the Caribbean and Southern colonies. They also needed laborers who would be less capable of escape and who would have little to no legal recourse in response to exploitation and abuse. As some European countries, particularly France, Spain, and Portugal, had already established trade with West African societies that had their own slave systems—albeit very different from that which would exist in North and South America—it made sense to request human cargo.

Though slavery was discontinued in some Caribbean colonies, particularly those managed by the British, in the early 1800s, it expanded in the United States after the Louisiana Purchase in 1803. Demand for cotton in textile mills in both New England and Great Britain required more slave labor, particularly in newly acquired territories such as Mississippi, Alabama, Arkansas, Louisiana, and East Texas—places that were especially hospitable to the cultivation of cotton.

Slavery took root in North America and the Caribbean because they were colonies. It was quite common in colonies for agrarian efforts to take the form of plantations. Plantations require a lot of labor, and slaves were cheap. Once you bought them, you never had to pay them and only had to feed them.

It's important to note that free laborers would not work the plantations.  They wanted to go off and work their own land (which they could get relatively cheaply).  This meant that the workers had to be forced into working.  That is where slavery and indentures servants come in.  On indentured servants, I'd add that they were white and generally English and therefore they felt that they had various rights that had to be respected  -- they were harder to push around.

Because it was the most economical and practical answer to the Southern colonies' need for a labor force.  With the kinds of cash crops that were grown on plantations there - tobacco, rice and indigo mostly - it required a labor intensive process of almost daily agricultural work and care.  Indentured servants were OK for a while, but they were temporary, usually finishing their contracts within 5 to 7 years, after which you had to rent and train another one.  Native Americans simply escaped and went home and could not be captured in the numbers needed.

With slaves, not only did the owners get a permanent worker, but they also were legally entitled to all of their offspring.  It was a very brutal and ugly institution, but in the 17th through the 19th centuries, it was the most economically viable solution to southern plantation owners' labor needs.