一 (yī): One, a single instance.
败 (bài): To be defeated, to lose, to fail.
涂 (tú): To smear, to spread, to daub; mud. This character is the most graphic part of the idiom.
地 (dì): The ground, the earth.
These characters combine to create a powerful and visceral image: a single defeat (一败) so total that it's as if the loser's brains and innards have been smeared (涂) all over the ground (地). The idiom originates from historical records describing the gruesome aftermath of a decisive battle, and it has retained that intensity ever since.
一败涂地 (yībàitúdì) is a strong, formal idiom, but it's widely understood and used in various modern contexts to add dramatic emphasis to a complete failure. Its connotation is always strongly negative.
Business and Finance: Used to describe a catastrophic business failure, a disastrous product launch, or a stock market crash where an investor loses everything.
Sports: A perfect term for when a team is not just beaten, but utterly humiliated and dominated by a far superior opponent.
Politics and Debates: Describes a political campaign that ends in a landslide loss or an argument where one side is completely dismantled and discredited.
Academics: Can be used, often hyperbolically, to describe a terrible performance on a major exam.