The Federalist Papers quote you provided addresses the complex legal and social status of slaves in the context of the ratification of the U.S. Constitution. The compromise that is relevant to this debate is the Three-Fifths Compromise. This compromise was reached during the Constitutional Convention of 1787 and determined how slaves would be counted for purposes of representation and taxation. Specifically, it stipulated that each slave would be counted as three-fifths of a person when determining a state's population for representation in Congress.
This compromise highlighted the tension between the recognition of slaves as property and their acknowledgment as members of society with certain legal protections, as described in the quote. It served as a way to appease both Northern and Southern states during the ratification process while addressing the contentious issue of slavery.