A prissy person likes things to be neat and tidy, and expects people to follow the rules and be extremely polite. If your prissy cousin invites you to a tea party, you'd better arrive on time and wear your white gloves.
Prissy people are extremely prim and proper, and they may also be so fastidious that the sight of your muddy dog running through the dining room will disgust them. You could also complain about your school's prissy dress code, which doesn't allow you to wear your Wonder Woman costume to math class. Prissy is thought to be a Southern US invention from the late 1800s, either rooted in precise, or a combination of sissy and prim.