It's often used when someone uses a phrase that is not commonly known or is new and original. It implies that the speaker is claiming credit for creating the phrase, although it may not be entirely new.
For example:
* "I'm feeling a little under the weather, to coin a phrase."
* "The company's new slogan is, to coin a phrase, 'Think outside the box'."
While "to coin a phrase" is used to imply originality, it's important to note that many phrases are not actually new. The speaker is simply using it to add a touch of humor or emphasis.