The enslavement of Africans was the result of the convergence of multiple factors. The first factor was the cut off of the slave trade from the east when Constantinople fell in 1453. Originally, Slavic and the people of the Caucuses provided the slave labor for the peoples of the Mediterranean.

The fall of Constantinople also complicated the spice trade because the trade routes were now controlled by the Ottoman Empire. In an effort to find a way around the Ottomans, the Portuguese and Spanish began to send expeditions to try to find new sea routes to the east. Along the way the Portuguese and Spanish conquered the islands of the Atlantic right off the African coast and set up forts on the African coast itself in order to trade with the Africans and resupply their ships. The trade originally centered around the gold at first and slaves were a secondary factor.

At the same time the cultivation of sugar had spread west to Spain and Portugal. Europe's sugar addiction was beginning and the Spanish and Portuguese saw a chance to cash in. The islands off of Africa were a perfect place to grow sugar because the climate was right. The problem was that sugar was a very labor intensive product. The Spanish and Portuguese tapped into the trading networks they had been using to get gold and instead got slaves. These slaves worked on plantations on the islands off of Africa and began to make a substantial profit.

At the same time the New World was "discovered" and the Spanish and Portuguese needed labor to extract the riches of the New World. They turned to the Native population but the Natives began to die off in large numbers due to disease or were running away. To replace them, the Spanish and Portuguese did what they did on their islands in Atlantic and applied it to the New World.

Inhuman Bondage by David Brion Davis has a great chapter about this very subject.

The triangular trade that occurred because of the sugar trade. Since sugar was so craved by Europeans in the 16th, and 17th century, they decided they need to find land they could grow it, as there is no suitable land in Europe. It's not common knowledge, but the original slaves used by the kingdoms were actually eastern European (takes from the word "Slav" meaning Slave.") One of the main reason for expropriation was sugar. When they discovered the Americas, the Caribbean islands were perfect for sugar. As there were no decent machines to harvest, manual labor provided cheap labor. This prompted western powers to colonize and create forts one the coast of west Africa to buy slaves from African and Arab slave traders and transported to the Americas (known as the Middle Passage). The original slave owners left slaves in terrible working conditions, meaning there were a high death rate. Fun fact, The American plantation system actually (contrary to popular belief) were much more... nicer if I must to slaves, and had a drastically lower death rate.

Source: Multiple history courses