Cajuns are an ethnic group consisting of French-Canadians who refused to accept British rule after the French and Indian war and were driven from Canada by the British, settling at various points along the Eastern seaboard where many assimilated into the existing communities.  However, an intact group found hospitable shores in Louisiana (which, as the name suggests, was once a French colony), where they remain a distinct ethnic population with their own language, customs, and beliefs.

Their French heritage means they are staunch Catholics, who embrace the "mysteries" of the church.  This heritage is also responsible for a laissez bon temps roulez attitude ("let the good times roll") and, of course, their famous spicy food (though real Cajun food is more about taste than about percentages of cayenne pepper).  An insular people, separated by both geography (often live in rural/swampy areas) and language (a kind of informal French), they value family and community and regard strangers with a suspicious eye.

In Louisiana during the period of the novel (they were little known outside of Louisiana before Chopin's tales spread word of their existence) their cultural connotation was a bit uneven.  The closest modern day comparison I can make is that they could be considered good-natured, religious hillbillies who know how to cook well: harmless, but easy to look down upon.