"(Our) peculiar institution"was a euphemism for slavery and the economic ramifications of it in the American South. The meaning of "peculiar"in this expression is "one's own", that is, referring to something distinctive to or characteristic of a particular place or people.
Peculiar Institution
"peculiar institution"
Peculiar Institution
A most peculiar institution
The New `Peculiar Institution':
A peculiar institution? Greco–Roman monogamy in global context
Peculiar institution : America's death penalty in an age of abolition
Peculiar institution : America's death penalty in an age of abolition
The New `Peculiar Institution':: On the Prison as Surrogate Ghetto
Peculiar institution: America's death penalty in an age of abolition [Book Review]
The Scottish Criminal Jury: A Very Peculiar Institution
Reason of Slavery: Understanding the Judicial Role in the Peculiar Institution
On the Renting of Persons: The Neo-Abolitionist Case Against Today's Peculiar Institution