These are example of coins that obtained damage after they where struck by a coin die, or coins which where damaged during the minting process. A true mint error coin is a planchet that strikes a coin with details that where not intended for that particular coin series.
In example, the famous 1955 Double Die, Lincoln Cent was created when the working die had a double image of the coins intended design. This doubling was passed on to the copper planchet as doubled features, on several coin, until the mint workers discovered the mistake and stop using the die.
Any other action against a coin during or after the strike is considered mint damage. However, if the damage is dramatic like fold over strikes, multiple strikes, die adjustment strikes, etc. then they are usually classified as mint errors. In this writers mind, it's a controversy that might never be resolved.
But die damage is still damage, no matter if accidental or not. If a coin get's jammed in the feeder and is struck several times and looks like something out of Frankenstein movie, doesn't make it any more a mint error than Strike Doubling where the die had a "loose bolt" and as it struck the planchet, jarred, thus creating coins like a Poor Man's Double Die which is actually machine "damage", and not considered a mint error.
However, for now, we will stick with what's most popular to ensure that the reader is not confused on the issue of what makes a mint error and what doesn't. Let us suffice to say, that a coin with details other than intended for the series or something happened to the coin during the minting process, and this "difference" can be verified that it happened at the mint, then it can be considered collectible. The more dramatic the mint error or mint damage the higher the market value.