Definition & Meaning of "[give] {sb} a run for {one's} money"

What is the origin of the idiom "give someone a run for their money" and when to use it?

The idiom "give someone a run for their money" is believed to have originated from horse racing, where a horse that is expected to win easily is challenged by another horse that runs just as fast and puts up a strong fight. Today, the idiom is often used in a figurative sense to describe a situation where someone competes with or challenges another person, organization, or team, and is so good that they make them work hard to win.