In the Ivalice Games, it deals damage equal to the amount of damage you have done with Knots of Rust. But each time you use a Dark Matter, the damage resets. In Final Fantasy IV, the use varies from version to version, in the DS version, it opens up a bonus boss, in all others, it does nothing.
Additionally, in most other games in the series, if used as an item, it deals an automatic 9999 damage to all or one of the enemies. It is also used in Final Fantasy IX to teach Garnet Odin.