Enslavement is the noun form of the verb "to enslave (sb)", in other words to make somebody into a slave. Slavery is the name of the system under which people are denied their own free will and treated as property. This term is more commonly used than enslavement.

‘Slavery' is the system where people are enslaved or a status of being a slave. For example, before the American Civil War, there was slavery in Southern America where many black Americans were sold into slavery. 'Enslavement' is the action of enslaving someone. For example, enslavement is never justified. Off course, neither is slavery because slavery legalises enslavement.