I like the following definition for
Social Fraternities and Sororities as provided by the University of Wisconsin-Madison Student Organization Office.
The term "social" in social fraternity and social sorority refers to social development. The original intent of these organizations when they began in the 18th Century was to assist students to become "socialized," that is, directed, with proper consideration of one's future responsibilities as a citizen in society. The individual and the organization's members base membership on mutual choice. Social fraternities and sororities are self-governing and self-supporting organizations.