“Coin” comes from the Latin cuneus, or “corner.” When the word first arose in English in the early 14th century, it meant “wedge,” but it quickly adopted the sense of “thing stamped” or “a piece of money” because dies for stamping metal were wedge-shaped.
“Coin” came to English by way of Old French, which first adopted the legal tender sense of the word. The English word has been variously spelled coyne, coign, coigne or quoin. (And the word “quoin” is still used today to refer to keystones and cornerstones of buildings.) In Modern French, the word *coin* still means “corner, angle, nook.”
The Old English word mynet (which would become the word “mint”) was also used to mean “coin, coinage, money”—or, as the contemporary word is most commonly used, the act of stamping coins or the place where coins are minted. It predates “coin” by about 600 years and comes from the Latin moneta, “place for coining money, mint; coined money, money, coinage.”
The stamping sense of the English “coin” loosely remains in the idiom “coin a phrase,” which originated in the 16th century and suggests establishing a cliché or a widely recognized term.
In some of its earliest recorded uses, the idiom often facetiously drew upon the concept that stamped coins were often counterfeited, in the sense that those who newly “coined” words and phrases claimed to have invented them, but actually drew them from other languages: “Young schollers not halfe well studied… will seeme to coigne fine wordes out of the Latin” (from The arte of English poesie, George Puttenham, 1589).
Shakespeare, of course, famously coined many new words—most often by filling lexical gaps in English. As the eponymous protagonist of his play Coriolanus said, “So shall my lungs coine words till their decay.”