Old English catt (c. 700) "domestic cat," from West Germanic (c. 400-450), from Proto-Germanic *kattuz (source also of Old Frisian katte, Old Norse köttr, Dutch kat, Old High German kazza, German Katze), from Late Latin cattus.
The near-universal European word now, it appeared in Europe as Latin catta (Martial, c. 75 C.E.), Byzantine Greek katta (c. 350) and was in general use on the continent by c. 700, replacing Latin feles. Probably ultimately Afro-Asiatic (compare Nubian kadis, Berber kadiska, both meaning "cat"). Arabic qitt "tomcat" may be from the same source. Cats were domestic in Egypt from c. 2000 B.C.E., but not a familiar household animal to classical Greeks and Romans. The nine lives have been proverbial at least since 1560s.
The Late Latin word also is the source of Old Irish and Gaelic cat, Welsh kath, Breton kaz, Italian gatto, Spanish gato, French chat (12c.). Independent, but ultimately from the same source are words in the Slavic group: Old Church Slavonic kotuka, kotel'a, Bulgarian kotka, Russian koška, Polish kot, along with Lithuanian katė and non-Indo-European Finnish katti, which is from Lithuanian.
Extended to lions, tigers, etc. c. 1600. As a term of contempt for a woman, from early 13c. Slang sense of "prostitute" is from at least c. 1400. Slang sense of "fellow, guy," is from 1920, originally in African-American vernacular; narrower sense of "jazz enthusiast" is recorded from 1931.
Cat's paw (1769, but cat's foot in the same sense, 1590s) refers to the old folk tale in which the monkey tricks the cat into pawing chestnuts from a fire; the monkey gets the roasted nuts, the cat gets a burnt paw. Cat burglar is from 1907, so called for stealth. Cat-witted "small-minded, obstinate, and spiteful" (1670s) deserved to survive. For Cat's meow, cat's pajamas, see bee's knees. For let the cat out of the bag, see bag (n.).
"small sack," c. 1200, bagge, probably from Old Norse baggi "pack, bundle," or a similar Scandinavian source. OED rejects connection to other Germanic words for "bellows, belly" as without evidence and finds a Celtic origin untenable. In some senses perhaps from Old French bague, which is also from Germanic.
As disparaging slang for "woman" it dates from 1924 in modern use (but various specialized senses of this are much older, and compare baggage). Meaning "person's area of interest or expertise" is 1964, from African-American vernacular, from jazz sense of "category," probably via notion of putting something in a bag. Meaning "fold of loose skin under the eye" is by 1867. Related: bags.
To be left holding the bag (and presumably nothing else), "cheated, swindled" is attested by 1793. Many figurative senses, such as the verb meaning "to kill game" (1814) and its colloquial extension to "catch, seize, steal" (1818) are from the notion of the game bag (late 15c.) into which the product of the hunt was placed. This also probably explains modern slang in the bag "assured, certain" (1922, American English).
To let the cat out of the bag "reveal the secret" is from 1760. The source is probably the French expression Acheter chat en poche "buy a cat in a bag," which is attested in 18c. French and explained in Bailey's "Universal Etymological English Dictionary" (1736), under the entry for To buy a pig in a poke as "to buy a Thing without looking at it, or enquiring into the Value of it." (Similar expressions are found in Italian and German; and in English, Wyclif (late 14c.) has To bye a catte in þo sakke is bot litel charge). Thus to let the cat out of the bag would be to inadvertently reveal the hidden truth of a matter one is attempting to pass off as something better or different, which is in line with the earliest uses in English.
Sir Joseph letteth the cat out of the bag, and sheweth principles inimical to the cause of true philosophy, by wishing to make great men Fellows, instead of wise men ["Peter Pindar," "Peter's Prophecy," 1788]