I will simply expand on the previous Educator's response, but I will add that free blacks who were kidnapped from Northern states in the nineteenth century also went through a process of "seasoning." Solomon Northrup writes about this in his memoir, 12 Years a Slave.

"Seasoning" often involved the use of a slave breaker—a white person whose job it was to condition a free human being to an enslaved state. The slave breaker has shown up in multiple historical narratives about slavery. Some examples include Mr. Covey in The Narrative of Frederick Douglass and the slave breaker who lashes Kunta Kinte with a whip until he learns that his name is "Toby" in Alex Haley's Roots.

Other aspects of "seasoning" include taking drums away from slaves (though some music and dancing were allowed on slave ships to provide the slaves with exercise), demanding that they learn to communicate in the languages of their masters, and instilling them with Christianity. Slave masters' reading of the Bible reinforced the notion that black people were the cursed sons of Ham or born with the mark of Cain—reinforcements of the belief that blackness was a mark of their destiny as slaves.

The purpose of seasoning is to break the spirit or will of a free human being to fight the condition of being enslaved. I do not think that "seasoning" convinced most black people that they belonged in the possession of whites, but it focused them on survival instead of resistance and convinced them that they were up against a nearly insurmountable power.

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.