What did the Ancient Egyptians expect the afterlife to be like?

The Ancient Egyptians were very concerned with the afterlife. 

They expected that once they were buried, they would have to fight through the perils of the underworld to the Weighing of the Heart, a ceremony involving Thoth, Anubis, Sobek, and Ma'at, where the human's heart would be weighed against one of Ma'at's feathers. If their heart was too light or too heavy, Sobek would eat it, denying them access to Osiris' kingdom. 

So not only did they have to worry about being a good enough person to get past the Weighing of the Heart, they had to get there. So, if you were rich enough, you made sure you were buried with a copy Book of the Dead, which contained spells that would help you through the underworld intact.

Mummification was very important here. They believed if say, the nose got damaged, they wouldn't be able to smell in the afterlife. Having a physical vessel long after they were dead meant having a corporal form in the afterlife.

To equate it to Christian terms: Osiris' kingdom was their heaven, but they had to fight to get there. Their judging ceremony was the Weighing of the Heart. If they failed to get there, or failed that, they would go to the Ancient Egyptian hell, which was eternity on Earth.