Today’s desk dictionaries often include this word, defining it as boldly disrespectful or impudent, not because it is current — it’s archaic, last used unselfconsciously in the seventeenth century — but because it was once common enough that readers are still likely to encounter it. Some writers — such as Sir Walter Scott — have since borrowed it to provide a bit of period flavour in historical novels.
It’s formed from the equally archaic apert, from Latin apertum, open, through French. The oldest English sense was “public, plain, unconcealed”, but this shifted over time until it came instead to mean outspoken and later insolent. (Through confusion with another French word, it could also mean clever.) Our word seems to have been created from apert in either the sense of a person who is outspoken or clever, since the mal- prefix means “improperly, badly, wrongly” (as in maladjusted or malodorous), so creating malapert, of somebody improperly outspoken or inappropriately clever. We still know apert in its aphetic form pert, which retains the idea of insolence, though weakened into cheekiness or impudence.
The idea was personified into Jack Malapert, an insolent person, which is in one of the first printed books in English, Caxton’s Book of Curtesye of about 1477-78. In modern form, the line would be “Don’t play Jack Malapert, that is, don’t be presumptuous”. The female equivalent was Miss Malapert, as in Henry Fielding’s play The Fathers: “Well, Miss Malapert, and what do you think you have said now? why, nothing more than that your grandmothers had ten times as much prudence as yourselves.”