The Akh (Ꜣḫ meaning '(magically) effective one'), was a concept of the dead that varied over the long history of ancient Egyptian belief.
It was associated with thought, but not as an action of the mind; rather, it was intellect as a living entity. The Akh also played a role in the afterlife. Following the death of the Khat, the Ba and Ka were reunited to reanimate the Akh. The reanimation of the Akh was only possible if the proper funeral rites were executed and followed by constant offerings. The ritual was termed: se-akh 'to make (a dead person) into an (living) akh.' In this sense, it even developed into a sort of ghost or roaming 'dead being' (when the tomb was not in order any more) during the Ramesside Period. An Akh could do either harm or good to persons still living, depending on the circumstances, causing e.g., nightmares, feelings of guilt, sickness, etc. It could be evoked by prayers or written letters left in the tomb's offering chapel also in order to help living family members, e.g., by intervening in disputes, by making an appeal to other dead persons or deities with any authority to influence things on earth for the better, but also to inflict punishments.
The separation of Akh and the unification of Ka and Ba were brought about after death by having the proper offerings made and knowing the proper, efficacious spell, but there was an attendant risk of dying again. Egyptian funerary literature (such as the Coffin Texts and the Book of the Dead) were intended to aid the deceased in "not dying a second time" and becoming an akh.
Read more about this topic: Ancient Egyptian Concept Of The Soul