What is the origin of the idiom "axe to grind" and when to use it?

The idiom "axe to grind" comes from a story by Charles Miner, published in 1815. In this story, a man falsely accused another of having an axe to grind and made it a metaphor for having a hidden agenda or personal interest in a matter. It is used to refer to someone who has a personal motive or vested interest in something rather than being objective or impartial.