The Egyptians believed that living things contained a Ka, which was sort of a generic spirit with no personality. The Ka would wander away from the body after death, but it wasn't really that person any more. Living things also contained a spiritual essence called the Ba, which contained your personality, your memories, and everything else that makes "you".
The Egyptians believed that their funeral rites released the Ba from the body, allowing it to freely join with the Ka to form an Akh. The Akh was your immortal ghost, as believers in many religions regard it today. You could only enter the afterlife if your Ka and Ba were both joined, setting your personality free and allowing your spirit to exist away from your body.
All of this came with a catch, however. While the Ba could be freed from the body, it still needed to obtain its energy and nourishment from the body every night, or it would die. This meant that the body had to be preserved permanently so the Ba would have a permanent place to gain sustenance, and it meant that the body had to be stored with enough food and goods to allow it to survive indefinitely on the "life essence" the Ba could extract from it. The Egyptians believed that we lived by consuming the life essence of other living things (i.e., when you eat a beet, it's not the vitamins keeping you alive, but your life essence absorbing the life essence of the plant).
That's why the Egyptians mummified anyone they cared about, and left elaborate graves with food and other goods for them. To the Egyptians, it was the only way they could ensure that their loved ones would live on.
That a grieving woman would want this done to her fetus is not a surprise. People today aren't all that different from the people who lived several thousand years ago, and people bury stillbirths today for largely the same reasons. Grief over a lost pregnancy is a human constant.
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