It is, alongside human teenagers who have been brought there, inhabited by beings which have been dubbed NPCs (Non Player Characters) by Yuri, as they make look and act human, but in reality, they have no souls.
No one knows who created the world, how the 'rules' are exactly determined, and why. What is equally as mysterious is how long the world has existed. There are theories that it has existed since forever. Despite the numerous enigmas that surround the world, it serves as a sort of second life for teenagers whose lives were filled with despair and pain. They are brought there after they have died and, alongside others, try to live there with fulfilled existences to make up for their pain. After, they disappear as their happiness has been granted. According to Yuri, it seems the only explanation for the existence of the world is created by God for a reason since there were no other possible theories or alternatives to explain the death of their lives ending up in the Afterlife School instead of ending up in Heaven, Hell, etc. Although never actually stated in the series, tt is currently unknown if anyone who has committed suicide can go there as no member in the SSS has killed themselves.
The time people arrive in the Afterlife doesn't seem to happen in chronological order as they die, such as when Otonashi arrived after Kanade or when Shiina, being one of SSS's first members, was actually from ancient Japan (era unknown).
Or, it could be simply said that time does not exist in the Afterlife and teenagers who died with regrets can go there, regardless what time of death or time period said person is. An example of the latter is Shiina: a girl who was from a period in time which Japanese citizens in Ancient Japan did not know the existence of God or any of the Abrahamic Religions yet she was able to appear in the Afterlife when she died.
There have been no explicit rules or laws in the Afterlife. However, it has been stated and shown many times a person cannot die there (it is unknown if NPCs also follow this rule). If they are killed, they wake up fully recovered as if they merely lost consciousness for a while, although they will experience the pain of it. There is also the fact that you can literally make things out of dirt while in the world that you could make in the real world, like how Guild creates weapons for the SSS (Though it was never shown had they did it in the anime). It is said to be impossible to make things there you didn't know how to make, such as when Guild tried to make a linear cannon to use against Angel and it exploded when they used it.
In the Heaven's Door manga, Chaa, the future founder of Guild, explained how he managed to have brought a gun in the afterlife shortly after their first meeting with Yuri, Hinata, and Ooyama. This is done by shaping clay from the walls of a man-made cave he discovered when he first arrived in the afterlife. The first to know of this method included Yuri, Hinata, and Ooyama through Chaa prior to the formation of SSS. In time, as shown in the anime the Guild forsaken this old method and instead automated weapon production based on the originals they made by hand.
It appears that most of the rules of the real world also hold the Afterlife together, such as no one can fly. Also, Yuri states that no one can age in the Afterlife, including the NPCs.
There are unidentified powers or creations that don't seem quite possible in the Afterlife, though, such as the computer program Angel Player (which can give a person supernatural abilities and change a person entirely) and Naoi's hypnotism.
No one knows what happens after someone in the Afterlife who finally disappears but in the end at Episode 13, it shows the person who vanishes will be reincarnated with the same appearance they had before they died, given the ending is canon (an alternative ending also existed where Otonashi stayed behind and became Student Council president).
The majority of the series takes place within the academy, presumably a high school. It is roughly around four stories tall. The academy is made up of classrooms, a computer lab, a cafeteria, a school garden, a gymnasium, a laundromat room, and dormitories. On the top floor is the school principal's office. Outside on school grounds is a sports field which is made up of a soccer field, a track, a long-jump pit, and a baseball field. Directly underneath the building, a large underground cavern which resembles an old mining cave stretches across the area and leads to underground caves far below the surface. There is also a large underground garden used by Kanade Tachibana to grow radishes and other vegetables.
The school is surrounded by forests and mountains, which stretch onto the horizon. It hasn't been identified how far they go, or if anything goes beyond that. In one direction, a large river runs by, where SSS members sometimes fish to obtain food. A gigantic black fish dubbed the "Monster Stream" used to roam the waters until Kanade slashed it into pieces and was eaten by the SSS and NPCs.
The world is inhabited by NPCs which are mostly that of high school students. There have been adults shown as well, such as the Principal in the manga, the technician replacing computers in the computer lab in Episode 12, and the teachers. There have not been any appearances of younger children, though.
Although they look and sound like a regular human, Yuri has commented that they are not. She explains that NPCs have been in the Afterlife from the very get-go, and by one example once tells Otonashi to go slap a girl on her ass and see if she'll react like a regular girl. Any weird things an NPC sees thinks that it is normal, or their reactions are programmed depending on the situation. One example was the NPC technician who replaced the stolen computers in Episode 12 didn't panic or act scared like a regular human when Yuri was pointing a submachine gun at him and strangely didn't seem to not notice the gun at all.
NPCs can be edited by the computer program "Angel Player", which is shown when the Shadows appear. The Shadows are large slightly humanoid clouds of dark colored matter, and they have reflexes that surpass humans. They can appear from the ground and leap long distances. When one catches onto a human, they can pull them into the ground, effectively turning them into an NPC as well the next time they are seen. They can be destroyed as shown when the SSS shoot them with bullets and Noda and Fujimaki cut them with a halberd and a shirasaya.
- There is no official name for the school located in the afterlife. The name "Heaven Academy" (天上学園, Tenjou Gakuen), however, can be seen as one of the paintings in the Principal's Office.
- It is unknown if any other teenagers, besides Japanese, can go there as the manga and anime did not list any SSS members or NPC students with foreign names.
- Since the Afterlife is based off a Japanese high school; such as sliding doors, language, and uniforms, it could be possible the Afterlife, fans have seen in both the Anime and Manga could be for Japanese students only (i.e the school roster that is seen in Episode 3 had all students with Japanese names). But since Angel Player is fully written in English, it could be false. But again, no confirmation actually exists.