Meaning: To introduce a common meaning or clichè. For example, "He is so wealthy, to coin a phrase, he was born with a silver spoon in his mouth."
The verb to coin originally meant to literally mint a coin. It dates to the 14th century. In the late-16th century, the sense generalized to become to create or invent something other than coin, including words and phrases. In 1940 the specific usage of the phrase to coin a phrase, used ironically to introduce a banal statement or clichè, came into use.
Some believe that usage of to coin in this fashion is actually an error, believing instead that it should be to quoin. This term is a printer’s term meaning to secure a block of type with a quoin, or metal wedge. So to quoin a phrase is to set it into type or make it permanent. But quoin is simply a spelling variant of coin that is primarily used in this specialized printing sense. The sense meaning to create is invariably spelled coin.
(Source: Oxford English Dictionary)