Here's the prim Professor Umbridge, from Harry Potter and the Order of the Phoenix. Harry immediately dislikes her. Her prim manner of speaking, the prim way she clears her throat before speaking ("hem, hem"), and her prim style of dress all just gross him out. She presents herself like a sweet, innocent young girl—all prim and proper—but she's actually pure evil.
So, that's the worst kind of primness: when someone acts primly, all dainty and cutesy, in a fake way that makes you want to barf.
But here's the best kind of primness: when someone acts primly, all wholesome and adorable, in a genuine way that makes you smile. Here's a prim young girl, Primrose Everdeen. "Prim" for short, she's Katniss's little sister in the Hunger Games series, and she embodies the good side of primness: she's neat, trim, tidy, clean, kind, gentle, and innocent. In Katniss's words, Prim's face is "as fresh as a raindrop," and "no one can help loving" her.