This has been asked before, so I'm linking you to those answers, which can be summarized in "African Slave trade was a trade between Europeans and Africans, where European luxuries were traded for African people." I'm just quoting the parts that answer your question, but I recommend reading it in its entirely:

1

African slaves were typically already slaves in Africa. In some parts of Africa human slaves were one of very few forms of wealth during the trans Atlantic slave trade. They were property that the Europeans purchased by means of other goods such as metals and textiles. Not to say kidnapping didn't happen, but it's definitely not as common as most people think. A slave for a slave is not necessarily a good deal especially when considering bringing over slaves to Africa would come at great cost to Native Americans intern affecting the Europeans bringing them over, and essentially it would be pointless when considering there was a vast able bodied population already there.

2

West Africa (where most of the slaves in the Americas came from) already had long standing traditions of 'slavery', although they were nothing like those systems that the Europeans and Americans would create. Europeans could easily purchase African slaves from other Africans along the coast. Africans were eager to sell their neighbors because they didn't really think of themselves as some kind of monolithic 'culture' in the way that Africans are usually grouped by people today. And again, Africans had been making servants out of one another for generations, there just were no moral obstacles to selling each other off to Europeans. The Europeans of course offered them valuable trade goods; such as firearms. Firearms would give a group an enormous advantage over their peers, so you can imagine they were highly sought after. It was a very favorable arrangement as far as most Africans were concerned, although in the long term it definitely depleted manpower from the region and caused a very unstable political organization, which made it very easy for European colonialists to dominate the region years later.

and

Its implied in the question (and a couple of answers) that Europeans had a sizable military presence that they used to control African populations and enslave them. For the most part this is untrue. For Europeans on the continent the slave trade was a economic affair, European traders attempted to source and negotiate for slaves rather than enslave them themselves. Initial contact with Africans would mean an integration into a much wider economic sphere. Before European (and Arab in some cases) contact African economic systems were limited to trading nearby. Archaeological evidence seems to suggest the main traded items were, Gold and Copper luxury goods and Iron tools. Slaves too were probably traded moderately. Post European contact the goods expanded to the exportation of goods to the coast in return for European luxury goods (cloths spices etc) and guns that couldn't be gained by Africans.

3

So over all, African leaders were essential to the slave trade. The cultures themselves adapted to the slave trade and developed their own way of raiding and transporting slaves. Slaves were a vital commodity to Africans and Europeans alike and the lifeblood of the economy in this period. From the Africans leaders perspective, they were not selling their people but rivals. I have neglected to mention the numerous societies that were actually importing slaves in this region and those that shunned the long distance European and Arab traders. Socities such as the Lozi and Kuba were not involved and maintained themselves well into the 19th century through importing African slaves. Nguni warrior societies (such as the famous Zulu) shunned the long distance trade preferring their insular way of life. Those two examples are testament to the immensity differences that exist in precolonial Africa. Hopefully this has given you some idea of what was behind the slave trade though.

4

In Africa, traditions of slavery had been going on for a very long time. Slavery was mostly personal and (relatively) humane, but debtors, criminals, and prisoners of war could be enslaved. European merchants stopping along the African coast on their way to Asia came into contact with this and were offered slaves while trading with the locals. Slaves were relatively cheap, and the slave trade expanded pretty rapidly in the 17th century. Soon European traders were buying slaves in mass after African slavers went around raiding for slaves and trading them for guns. In the American colonies these slaves faced horrible conditions and those that survived the voyage might not live a year working on Caribbean plantations. It didn't matter to the slavers, they were cheap and there were lots of them!

I'm concerned with the time of the trans-Atlantic slave trade, I'm aware that virtually every culture has owned slaves historically and treated them with varying degrees of respect.