Seasoning, in this context, refers to the process of making Africans into slaves. It does not refer to the process of buying slaves and bringing them across the ocean. Rather, it refers to the process of trying to instill in them the mentality that went with being a slave.
Africans who were captured and sold into slavery had, of course, not been born as slaves. They had been born as free people and would not have had the habit of acting and thinking like slaves. It was necessary for them to be “seasoned” so that they would come to have the characteristics of slaves. In other words, they had to be mentally and emotionally “broken” if possible, to make them act like slaves.
The process of seasoning, in its most basic sense, involved impressing on the newly taken slaves that they were helpless. It involved imposing strict discipline on them and showing them that breaking the rules would lead to harsh punishments. Ideally, from the slave owner’s point of view, seasoning would then proceed to convince the Africans to internalize the values and outlook of their white owners. That way, they would not need to be controlled solely by fear.
Thus, “seasoning” in the context of African American history is the process that Africans were put through in an attempt to make them have the mental attitudes consistent with being enslaved.