Execration is a sinister form of magic that involves destroying a small representation of the target to completely erase the target. It can be used against gods, though it only banishes gods deep into the Duat typically. A form of execration called shadow execration can destroy a god completely but is difficult magic and requires the god's shadow or sheut to work.
Execration can be used to stave much greater spells, so that the execration of a minor demon can generate enough power to summon and trap Set inside a malachite vase. The spell requires using the target's secret name. The spell can also be used to banish a god deep into the Duat by destroying a shabti of said god in the god's presence, but the more powerful the god, the more power it takes to perform and the magician can burn up from using all of their life force to do it. This happened to Michel Desjardins who used an execration to temporarily banish Apophis into the Duat to buy the Kanes some more time to teach the Path of the Gods. This execration only lasted a few days to weeks before Apophis returned again. While performing the execration, a shield of sorts formed around Desjardins and absorbed all attacks thrown at him by Apophis.
The evil magician Setne discovered a way to destroy any being in existence; including gods and Apophis by using an execration on their sheut. This is called a shadow execration. The shadow is part of the soul, like a back-up copy of it and also represents your legacy upon the world. If that is destroyed in an execration, the being it belongs to is destroyed as well. The gods are aware of this and keep knowledge of the sheut's true nature from mortals as a result with it being forbidden to even talk about it with them as the gods fear their sheuts being captured and used to blackmail or destroy them. Despite Setne making it sound complicated, this version of an execration, called a shadow execration is actually rather simple: the person needs to bind the sheut to a shabti, which is easy, with the hard part being actually finding the sheut which the gods hide and then they need to cast a normal execration on the sheut in the god's presence.
An execration can also be used in reverse to restore a being. In this case, the person needs to capture the being's sheut and then cast a reverse execration. Unlike a regular or shadow execration, this can be cast from a distance as it is a beneficial spell. The reverse execration will restore the being's sheut to them and their soul will be fully restored.
While raiding Vladimir Menshikov's study for the second part of the Book of Ra, Carter and Sadie witness him using an execration on a demon called Death-to-Corks to generate enough power to summon Set. This surprises them as Menshikov is supposedly a loyal magician of the House of Life and summoning gods is against the law.
After Apophis escapes from his prison and rises in Menshikov's body, a desperate Michel Desjardins uses a makeshift shabti of Apophis to cast an execration on him. Desjardins uses up all of his life force in the attempt and dies later as a result, but the execration banishes Apophis deeper into the Duat and it will take him a few weeks to a month to return, giving the Kanes time to prepare.
Carter and Sadie's back-up plan if they can't find a way to stop Apophis is to perform an execration on him. The two hope that with the two of them together, they will be able to banish him so deep into the Duat he can never return, but know it likely won't work and will cost them their lives to try.
After Apophis destroys Setne's version of the Book of Overcoming Apophis, they realize that he may have come up with a way to destroy a being by execrating their shadow or sheut and it could be used to destroy Apophis. Thoth confirms that this is possible and says its called a shadow execration. With the help of Setne, Carter, Sadie and Zia Rashid work to get Apophis' shadow to perform a shadow execration to destroy him. They retrieve the shadow and bolstered by the power of Horus and Isis, perform the shadow execration during the final battle. Like hoped, the shadow execration completely destroys Apophis and they survive, though magically exhausted.
After getting Bes' shadow to restore his ren, Walt Stone orders Sadie to return it to him by using a reverse execration. Sadie is able to reverse the wording of an execration so that the spell restores Bes instead of erases him. The reverse execration works and Bes is restored.