Eradication is the power or ability to completely exterminate an entity's essence. Therefore, the victim is not transported to either Hell or Heaven based on its moral alignment, but is instead completely wiped out from existence, leaving no trace behind. To humans, it would be equivalent to the destruction of their souls.
This ability has been featured in "Weaponizer", when Lucifer killed his brother, Uriel, with Azrael's blade, thus eradicating him from existence. It is also worth noting that the blade can affect even celestial beings, such as angels and Gods.