The phrase "Double Die" usually refers to improperly minted coins.
When a coin is minted, it is struck with what is referred as a "Die." The die is the actual image to be imprinted on the coin, and is contained in the molds at each of the mints. A Double Die coin is an error in which the coin is actually struck twice with the Die. In most cases, the coin displays a duplicate image with one slightly off-center. It looks sort of like an echo, or a blur.
Double Die strikes happen very rarely, and as a result, the double die coins are equally rare.
The most famous double dies are the 1955 and 1972 United States double die pennies.
United States Coinage