After defeating any villain, like an akumatized villain, Ladybug throws the object she got using Lucky Charm into the air, yelling "Miraculous Ladybug!" This generates an explosion of pink energy, eventually dispersing into small ladybugs that fly around Paris and fix any damage done since the appearance of the villain, including reverting death.
As indicated in the third issue of Miraculous Adventures, the Miraculous Ladybug might be able clean up any damage, not just damage caused by a villain. Victory and other superheroes expect the Miraculous Ladybug can clean up their catastrophic damage in order to destroy the Trash Krakken, but Ladybug worries if it will be able to restore that much damage.
While using Lucky Charm causes Ladybug to start losing power, using Miraculous Ladybug does not, it being an optional power she can use before she detransforms.
In the Korean version, the Miraculous Ladybug power is called "Miraculous Healing Light."
The Miraculous Ladybug not only fixes the villain's damage but can also fix the damage done by Cat Noir's Cataclysm and other general problems; for example, it fixes Alix's broken watch and rejoins the double Ladybugs and Timebreakers created by time travel in "Timebreaker".
However in "Dark Cupid", the poster of Adrien which a mind-controlled Sabrina was vandalizing wasn't reverted by Ladybug's power, meaning that not all non-magical effects caused by an akuma attack can be fixed by Miraculous Ladybug.
In "The Bubbler", despite using Lucky Charm to create a phonograph record, Ladybug doesn't utilize the Miraculous Ladybug before she detransforms. She also doesn't utilize it with the pen in "The Dark Owl" or the teapot in "Sapotis".
↑November 2015 per Thomas Astruc in https://twitter.com/thomas_astruc/status/666886344602423296
Kartos "@Thomas_Astruc can Ladybug revert or heal injuries and death inflicted by akumas with her "fixing" power?"
Astruc "@Kartos Anything"
Kartos "@Thomas_Astruc :O I'm assuming the amount of time she can go back to "undo" is very limited?"
Astruc "@Kartos limited to the apparition of the akumatized villain."