We have all known prigs, and some of us have been one.
The word prig (pronounced as you would imagine) identifies someone who is arrogantly, smugly, and obnoxiously concerned with conformity to some set of conventions and proprieties. It is rather more common in British usage than American, despite the widespread priggishness throughout our broad republic.
The Oxford English Dictionary is rather at a loss about its etymology, but shows that its development from the sixteenth century on has taken some interesting turns.
For example, the OED cites a source from 1567 that identifies tinkers as prigs: "These dronken Tynckers called also Prygges, be beastly people." In that era and into the seventeenth and eighteenth century, prig was a term for a thief, such as a pickpocket. Henry Fielding in Jonathan Wild, 1743: "The same Inducements have often composed the Statesman and the Prig, for so we call what the Vulgar name a Thief."
At the same time, the word was developing a separate identity, naming a dandy or fop. Richard Steele in the Tatler, 1709: "A Cane is Part of the Dress of a Prig," and in an 1835 dictionary: "In common language a Prig is a young Coxcomb, and has the adjective and adverb Priggish and Priggishly."
The current dominant sense, defined comprehensively in the OED as "A person who is offensively punctilious and precise in speech or behaviour; a person who cultivates or affects supposedly correct views on culture, learning, or morals, which offend or bore others; a conceited or self-important and didactic person," also has its roots in the seventeenth and eighteenth centuries. Tobias Smollett writes in 1753: "The templar is generally speaking a prig; so is the abbé: both are distinguished by an air of petulance and self-conceit, which holds a middle rank betwixt the insolence of a first rate buck, and the learned pride of a supercilious pedant."
Readers of this blog will recognize how neatly the definition fits the peeververein, with their self-important and misinformed strictures on English grammar and usage.
Example: From Clyde Haberman's review of Cinema Paradiso in The New York Times, 1990: "There, the Cinema Paradiso theater is the community center, a place to act up or to act out and to see some wonders from the outside world to the extent permitted by the local Roman Catholic priest. Don Adelfio screens all new movies first, and he is a scissors-wielding prig, snipping out any scene – certainly every kiss – that might send young blood racing."