If you coin a phrase, that means you come up with a new way to say something, like the person who coined "webizens" to describe people who constantly use the Internet.
The verb coin literally refers to making coins, the change you probably have in your pocket. The word can be used in a broader sense — creating something new, usually something related to language. For example, you could coin a phrase or a new word for “joke.” The language authorities would be proud — unlike federal authorities if you tried to coin money. That kind of coining is a criminal offense.