The following is from Pride and Prejudice:
Mr. Bennet was so odd a mixture of quick parts, sarcastic humour, reserve, and caprice, that the experience of three-and-twenty years had been insufficient to make his wife understand his character.
What does the phrase quick parts mean?
According to thesaurus.com, quick parts is a synonym of intelligence or wisdom:
[Nouns] intelligence, capacity, comprehension, understanding; cuteness, sabe [U.S.], savvy [U.S.]; intellect; nous, parts, sagacity, mother wit, wit, esprit, gumption, quick parts, grasp of intellect; acuteness; acumen, subtlety, penetration, perspicacy, perspicacity; discernment, due sense of, good judgment; discrimination; cunning; refinement (taste).
And the Moby Thesaurus II gives it as one of nearly 300 synonyms for sharpness.
An example from 1852's Home and Social Philosophy:
A man of quick parts may, indeed, strike out new and correct ideas upon a subject concerning which he is generally ill-informed; but if he wish that his idea should be useful, he must place it in the hands of one of the world's workers, who has spared no pains to teach himself upon that special subject all that his brethren know.
And from 1860's Contributions to the Edinburgh Review:
The truth is that, though Barère was a man of quick parts, and could do with ease what he could do at all, he had never been a good writer. In the day of his power he had been in the habit of haranguing an excitable audience on exciting topics.
In addition to Hugo's fine answer here are some more details: If you look at etymology you'll find
quick
O.E. cwic "living, alive," from P.Gmc. *kwikwaz (cf. O.Fris. quik, O.N. kvikr "living, alive," O.H.G. quec "lively," Ger. keck "bold"), from PIE base *gwiwo- "to live" (see bio-). Sense of "lively, swift" developed by c.1300, on notion of "full of life."part
c.1000, "part of speech," from O.Fr. part, from L. partem (nom. pars, gen. partis) "part, piece, side, share," related to L. portio "share, portion," from PIE base *per- "to assign, allot" (cf. Gk. peprotai "it has been granted," Skt. purtam "reward," Hittite parshiya- "fraction, part").
In usage you would say a person of quick parts.
Combining the meaning and usage it is plausible that the original meaning was "lively (witty, eloquent) speech (responses, oratory skills)".
Examining books on usage I found Webster 1832, treat it like this
Quick
4. Active ; brisk ; nimble ; prompt ; ready. He is remarkably quick in his motions. He is a man of quick parts
However that does not seem to shed the light on it, perhaps this passage shows a more detailed interpretation
He is grave with the grave, and lively with the gay ; to the man of quick parts he is quick and penetrating
The use of the idiom seems to be steadily declining over the past two centuries and is rarely used these days.
