Propriety is following what is socially acceptable in speech and behavior. If you are someone who cares about always doing the right and proper thing, your friends might accuse you of being obsessed with propriety and beg you to loosen up.
In the Victorian Age, both sexes had well-defined roles and were expected to exercise self-restraint. Except for the men. Everyone looked the other way when they went out on benders. Their wives at home however, were so confined by the era's standards of propriety that if a woman so much as referred to the fact that she was pregnant, everyone would cover their mouths and gasp. She'd committed an impropriety.