Excellent question, actually. Even many English speakers don't know how to use societal properly although social is a common adjective. Societal is the adjective that applies to all of society. "Societal normes dictate that we wear clothes in public". Social tends to be more personal, one's relationship to society. For instance, one speaks of one's social life.
To say that mariage is something social implies that it changes one standing with one's friends, with one's family, with one's relationships in general, far beyond the direct personal ramifications. To say that mariage is something societal implies that it has a legal, religious, traditional role with regard to the institutions of society in general.
Hope that helps.