"(Our) peculiar institution" was a euphemism for slavery an 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. The proper use of the expression is always as a possessive, e.g., "our peculiar institution" or "the South's peculiar institution". It was in popular use during the first half of the 19th century, especially in legislative bodies, as the word slavery was deemed "improper," and was actually banned in certain areas.