A prig is someone who is annoyingly smug in his or her moral behavior or attitudes. The word also can refer to one who is annoyingly fastidious about rules and small details. Whichever definition applies, the key word is annoying.
In William Makepeace Thackeray's Vanity Fair, Captain Dobbin relays a message from George Osborne to old Mr. Sedley:
"O, THAT'S your errand, is it?" cried the old man, jumping up. "What! perhaps he condoles with me, does he? Very kind of him, the stiff-backed prig, with his dandified airs and West End swagger. He's hankering about my house, is he still? If my son had the courage of a man, he'd shoot him."