prima donna n.

late 14c., "first, original, first in order of time," from Old French prime and directly from Latin primus "first, the first, first part," figuratively "chief, principal; excellent, distinguished, noble" (source also of Italian and Spanish primo), from Proto-Italic *prismos, superlative of PIE *preis- "before," from root *per- (1) "forward," hence "in front of, before, first, chief."

The meaning "of fine quality, of the first excellence" is from c. 1400. The meaning "first in rank, degree, or importance" is from 1610s in English. Arithmetical sense (as in prime number, one indivisible without a remainder except by 1) is from 1560s; prime meridian "the meridian of the earth from which longitude is measured, that of Greenwich, England," is from 1878. Prime time originally (c. 1500) meant "spring time;" the broadcasting sense of "peak tuning-in period" is attested by 1961.

c. 1200, "a mother," also "a woman of rank or high social position; superior of a convent," and an address for a woman of rank or position, used respectfully to other ladies, from Old French dame "lady, mistress, wife," from Late Latin domna, from Latin domina "lady, mistress of the house," from Latin domus "house" (from PIE root *dem- "house, household").

From early 14c. as "a woman" in general, particularly a mature or married woman or the mistress of a household. Used in Middle English with personifications (Study, Avarice, Fortune, Richesse, Nature, Misericordie). In later use the legal title for the wife of a knight or baronet.

Slang sense of "woman" in the broadest sense, without regard to rank or anything else, is attested by 1902 in American English.

We got sunlight on the sand

We got moonlight on the sea

We got mangoes and bananas

You can pick right off the tree

We got volleyball and ping-pong

And a lot of dandy games!

What ain't we got?

We ain't got dames! 

[Richard Rodgers, "There Is Nothin' Like a Dame," 1949]

"first," Italian fem. of primo "first" (see primo); used in various imported phrases in music and theater, such as prima donna,  prima ballerina (1799).