It tells the story of Re the sun god travelling through the underworld, between the time the sun sets in the west and rises again in the east. It is understood that the dead pharaoh is taking this same journey, ultimately to unify with the sun god and become immortal.
The underworld is divided into twelve hours of the night, each presenting various allies and enemies for the pharaoh/sun god to encounter. The Amduat names all of these entities, totalling many hundreds of gods and monsters. In fact, this is a prime purpose of the Amduat: to provide the names of these creatures to the spirit of the dead pharaoh, so he can call upon them for aid or use their name to defeat them.
The earliest complete version of the Amduat is found in the tomb of Thutmose III.