The Conception of the Soul
Ancient Egyptian have eight different parts of the soul.
The Khet, representing the physical body.
The Sah, representing the spiritual body.
The Ren, representing the name or identity.
The Ba, representing the personality.
The Ka, representing the "double".
The Ib, representing the heart.
The Sheut, representing the shadow.
The Sekhem, representing the power.
These eight parts are what make up your soul.
The Khet represents the physical body, which had to exist for the rest of the soul to have intelligence and the chance to be judged by the guardians of the underworld. This is the reason why bodies in Ancient Egypt were preserved the way they were. In the Old Kingdom period (circa. 2700-2200 BC) only the pharaoh were given the ability to be mummified, although all dead were given the honor during the Middle Kingdom period (circa. 2040-1782 BC).
Before you were allowed to be judged by the Netjer, your Khet needed to be "awakened". This manifested itself in the various funerary rites designed to reanimate the corpses in the afterlife. These rites were described in various texts, such as the Pyramid Texts, the Book of the Dead, and the Coffin Texts.
If every funerary rite was successful and Wasir finds the deceased person worthy, the Sah is formed. This spiritual body is your own body, but able to interact with the various beings in the afterlife.
The Sah was sometimes considered to also be a vengeful spirit, seeking revenge against those who wronged them during life.
Considered the most important part in Ancient Egypt, your Ib (heart) is the key to the afterlife. Without it, you wouldn't be able to survive death in the underworld. Ancient Egyptians didn't distinguish between the mind and the heart when it came to emotion or thought: the heart was the throne of emotion, thought, will, and intention.
The Ib would be examined by Anpu and the 42 Assessors of Ma'at after crossing the Duat. To gain entrance to the Kingdom of Wasir (Aaru), you would address each of the Assessors by name and recite each of the 42 Divine Confessions, and that you did not break them. Then your heart would be weighed against the feather of Ma'at. If your heart balanced with the feather, you would be able to continue to Aaru. If it was heavier, it was then devoured by Ammit, and your soul would be either eternally restless, or permanently destroyed.
More on the Weighing of the Heart ceremony later.
Your Ka is what distinguishes between a living person and a dead person, also called your "essence". When Khnum creates the bodies of children and places them in the mother's womb, either Heqet or Meskhenet gifted the baby with their Ka upon their birth, making them alive. Ancient Egyptians believed that you were truly alive after your birth, when either goddess breathed your Ka into you.
Your Ka is sustained through food and drink. This is why many coffins often have food and drink offerings.
Your Ba is your personality, and it takes the form of a bird with a human head. Not only is the Ba your personality, it is everything that makes an individual unique (in this sense, inanimate objects could also have a Ba).
This is your shadow. Because your Sheut always follows you around, it is said to represent something important about you. Because of this, statues of people or the Netjer were referred to as their Sheut.
There isn't much known about the Sekhem. Scholars sometimes define it as the life-force of the soul that exists in the afterlife after all judgement has taken place. But the Book of the Dead describes the Sekhem as the "power", and also as a place where Heru and Wasir dwell in the underworld.
Your name was given to you at birth, and the Egyptians believed it would live for as long as it was spoken. This is why there was so much effort to preserve names in writing
The Ren is a person's identity, experiences, and an entire life's worth of memories. A part of the Book of the Dead was a means to make sure the name survived. Cartouches (more coming in Important Kemetic Objects) often surrounded names to protect them from harm. On the opposite side, the names of enemies were hacked from monuments and had their recordings destroyed.
Although not mentioned before, the Akh is a belief that varied throughout the years of the Egyptian Empire. It was associated with thought. Not as an action of the mind, but as intellect as a living entity. The Akh also played a role in the afterlife: following the death of the Khet, the Ba and Ka would reunite to form the Akh. The reanimation of the Akh was only possible if all the proper funeral rites were executed and followed by constant offerings.